MATHEMATISCHE ANNALEN, ISSN 0025-5831, 02/2020, Volume 376, Issue 1-2, pp. 289 - 358

.... The formula explicitly relates such dimension to the Kazhdan-Lusztig representations associated with certain right cells of the Weyl group...

SUPERCUSPIDAL REPRESENTATIONS | ORBITAL INTEGRALS | PRIMITIVE-IDEALS | Primary 11F70 | FINITE CENTRAL EXTENSIONS | CONJECTURE | CHARACTERS | Secondary 22E50 | MATHEMATICS | STANDARD MODULES | UNRAMIFIED REPRESENTATIONS | COEFFICIENTS | 20C08 | LANGLANDS QUOTIENT THEOREM

SUPERCUSPIDAL REPRESENTATIONS | ORBITAL INTEGRALS | PRIMITIVE-IDEALS | Primary 11F70 | FINITE CENTRAL EXTENSIONS | CONJECTURE | CHARACTERS | Secondary 22E50 | MATHEMATICS | STANDARD MODULES | UNRAMIFIED REPRESENTATIONS | COEFFICIENTS | 20C08 | LANGLANDS QUOTIENT THEOREM

Journal Article

Journal of the American Mathematical Society, ISSN 0894-0347, 04/2014, Volume 27, Issue 2, pp. 437 - 477

.... Our classification shows that stable functionals arise from \mathbb{Z}. These automorphisms also appear in the Langlands parameters of epipelagic representations, in accordance...

Integers | Isotropy | Homomorphisms | Algebra | Mathematical theorems | Quotients | Center of gravity | Adjoints | Mathematical vectors | Automorphisms | P-ADIC GROUPS | SUPERCUSPIDAL REPRESENTATIONS | FORMAL DEGREES | MATHEMATICS | REDUCTIVE GROUPS | MINIMAL K-TYPES

Integers | Isotropy | Homomorphisms | Algebra | Mathematical theorems | Quotients | Center of gravity | Adjoints | Mathematical vectors | Automorphisms | P-ADIC GROUPS | SUPERCUSPIDAL REPRESENTATIONS | FORMAL DEGREES | MATHEMATICS | REDUCTIVE GROUPS | MINIMAL K-TYPES

Journal Article

Bulletin of the Iranian Mathematical Society, ISSN 1018-6301, 08/2017, Volume 43, Issue 4, pp. 291 - 311

Journal Article

Journal of the American Mathematical Society, ISSN 0894-0347, 04/2017, Volume 30, Issue 2, pp. 495 - 559

.... Let C be an algebraically closed field of characteristic p. We give a complete classification of irreducible admissible C-representations of G=\mathbf {G}(F...

Reductive groups | Admissible | Supercuspidal | Supersingular | Modulo p representations | HECKE MODULES | supercuspidal | PARABOLIC INDUCTION | ALGEBRA | supersingular | MATHEMATICS | admissible | reductive groups | GL(N) | SATAKE ISOMORPHISM | MODULAR-REPRESENTATIONS | RHO | LOCAL-FIELD

Reductive groups | Admissible | Supercuspidal | Supersingular | Modulo p representations | HECKE MODULES | supercuspidal | PARABOLIC INDUCTION | ALGEBRA | supersingular | MATHEMATICS | admissible | reductive groups | GL(N) | SATAKE ISOMORPHISM | MODULAR-REPRESENTATIONS | RHO | LOCAL-FIELD

Journal Article

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, ISSN 1073-7928, 06/2019, Volume 2019, Issue 11, pp. 3580 - 3620

We study the dimension of the space of Whittaker functionals for depth zero representations of unramified covering groups...

SUPERCUSPIDAL REPRESENTATIONS | MATHEMATICS | TORI | THEOREM | CONSTRUCTION | REDUCTIVE GROUPS | UNIQUENESS

SUPERCUSPIDAL REPRESENTATIONS | MATHEMATICS | TORI | THEOREM | CONSTRUCTION | REDUCTIVE GROUPS | UNIQUENESS

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 6/2016, Volume 283, Issue 1, pp. 169 - 196

In this paper we study the local theta correspondences between epipelagic supercupsidal representations of a type I classical dual pair $$(G,G')$$ ( G , G ′ ) over p-adic fields...

22E47 | Local theta correspondence | Mathematics, general | Mathematics | Epipelagic supercuspidal representation | Moment map | Stable vector | 22E46

22E47 | Local theta correspondence | Mathematics, general | Mathematics | Epipelagic supercuspidal representation | Moment map | Stable vector | 22E46

Journal Article

Taiwanese Journal of Mathematics, ISSN 1027-5487, 8/2015, Volume 19, Issue 4, pp. 995 - 1029

Following a construction of Gross and Reeder, we define simple supercuspidal representations of GL( ) over a 𝔭-adic field...

Coefficients | Mathematical vectors | Matrices | New vector | Matrix coefficient | Simple supercuspidal representation | MATHEMATICS | LANGLANDS PARAMETERS | CUSPIDAL REPRESENTATIONS | LINEAR GROUP

Coefficients | Mathematical vectors | Matrices | New vector | Matrix coefficient | Simple supercuspidal representation | MATHEMATICS | LANGLANDS PARAMETERS | CUSPIDAL REPRESENTATIONS | LINEAR GROUP

Journal Article

Journal of the American Mathematical Society, ISSN 0894-0347, 4/2007, Volume 20, Issue 2, pp. 273 - 320

Equivalence relation | Haar measures | Algebra | Mathematical theorems | Real numbers | Mathematical induction | Exhaustion | Fourier transformations | Eigenfunctions | P-adic groups | Supercuspidal representations | K-types | P-ADIC GROUPS | MATHEMATICS | CLASSICAL-GROUPS | BRUHAT-TITS THEORY | MINIMAL K-TYPES | FIELD | EXPANSIONS | ALGEBRA | GLN | CHARACTERS

Journal Article

Journal of Number Theory, ISSN 0022-314X, 03/2016, Volume 160, pp. 117 - 147

.... In this paper, we first present a simple proof and construction of the local Langlands correspondence for simple supercuspidal representations of GL (F), when p∤n...

Epipelagic supercuspidal representations | Langlands correspondence | Local converse problem | Simple supercuspidal representations

Epipelagic supercuspidal representations | Langlands correspondence | Local converse problem | Simple supercuspidal representations

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2017, Volume 290, Issue 1, pp. 247 - 255

We show that, in the setting of Galois pairs, the spherical characters of unitary supercuspidal representations satisfy an orthogonality relation.

Supercuspidal representation | Spherical character | MATHEMATICS | supercuspidal representation | spherical character | ADIC SYMMETRICAL SPACES | Mathematics - Representation Theory

Supercuspidal representation | Spherical character | MATHEMATICS | supercuspidal representation | spherical character | ADIC SYMMETRICAL SPACES | Mathematics - Representation Theory

Journal Article

Journal of the European Mathematical Society, ISSN 1435-9855, 2018, Volume 20, Issue 11, pp. 2813 - 2858

.... Using Poincare series, we globalize supercuspidal representations of H-F in such a way that we have control over ramification at all other places, and such that the notion of distinction with respect...

Local Langlands correspondence | Globalization | Supercuspidal representations | Function fields | GAMMA-FACTORS | local Langlands correspondence | MATHEMATICS, APPLIED | function fields | CLASSICAL-GROUPS | TAMAGAWA NUMBERS | PARAMETERS | CONJECTURE | P-ADIC GROUPS | ALGEBRAIC-GROUPS | MATHEMATICS | DISCRETE-SERIES | REDUCTIVE GROUPS | supercuspidal representations

Local Langlands correspondence | Globalization | Supercuspidal representations | Function fields | GAMMA-FACTORS | local Langlands correspondence | MATHEMATICS, APPLIED | function fields | CLASSICAL-GROUPS | TAMAGAWA NUMBERS | PARAMETERS | CONJECTURE | P-ADIC GROUPS | ALGEBRAIC-GROUPS | MATHEMATICS | DISCRETE-SERIES | REDUCTIVE GROUPS | supercuspidal representations

Journal Article

Journal of Algebra, ISSN 0021-8693, 06/2014, Volume 408, pp. 1 - 27

Using Bruhat–Tits theory, we analyze the restriction of depth-zero representations of a semisimple simply connected p-adic group G to a maximal compact subgroup K...

Representation theory | Branching rules | Bruhat–Tits theory | p-adic groups | 20G05 | P-adic groups | Bruhat-Tits theory | SUPERCUSPIDAL REPRESENTATIONS | MATHEMATICS | SL2(K) | MINIMAL K-TYPES | PRINCIPAL SERIES REPRESENTATIONS | P-ADIC FIELD

Representation theory | Branching rules | Bruhat–Tits theory | p-adic groups | 20G05 | P-adic groups | Bruhat-Tits theory | SUPERCUSPIDAL REPRESENTATIONS | MATHEMATICS | SL2(K) | MINIMAL K-TYPES | PRINCIPAL SERIES REPRESENTATIONS | P-ADIC FIELD

Journal Article

Publications mathématiques. Institut des hautes études scientifiques, ISSN 1618-1913, 2012, Volume 115, Issue 1, pp. 185 - 323

Let E/F be a quadratic extension of number fields. We study periods and regularized periods of cusp forms and Eisenstein series on over a unitary group of a...

INVARIANT DISTRIBUTION VECTORS | SUPERCUSPIDAL REPRESENTATIONS | MATHEMATICS | BASE CHANGE | PLANCHEREL MEASURES | REDUCTIVE SYMMETRICAL SPACES | RELATIVE KLOOSTERMAN INTEGRALS | GENERALIZED PRINCIPAL SERIES | TRACE FORMULA | IRREDUCIBLE REPRESENTATIONS | FUNDAMENTAL LEMMA

INVARIANT DISTRIBUTION VECTORS | SUPERCUSPIDAL REPRESENTATIONS | MATHEMATICS | BASE CHANGE | PLANCHEREL MEASURES | REDUCTIVE SYMMETRICAL SPACES | RELATIVE KLOOSTERMAN INTEGRALS | GENERALIZED PRINCIPAL SERIES | TRACE FORMULA | IRREDUCIBLE REPRESENTATIONS | FUNDAMENTAL LEMMA

Journal Article

ALGEBRA & NUMBER THEORY, ISSN 1937-0652, 2018, Volume 12, Issue 10, pp. 2327 - 2386

.... Given an irreducible cuspidal representation of G, we determine its Langlands parameter...

local Langlands correspondence | p-adic group | endoparameter | types and covers | CONTRAGREDIENT SUPERCUSPIDAL REPRESENTATIONS | SEMISIMPLE TYPES | CHARACTERS | MATHEMATICS | SMOOTH REPRESENTATIONS | Jordan block | DISCRETE-SERIES | GL(N) | symplectic group

local Langlands correspondence | p-adic group | endoparameter | types and covers | CONTRAGREDIENT SUPERCUSPIDAL REPRESENTATIONS | SEMISIMPLE TYPES | CHARACTERS | MATHEMATICS | SMOOTH REPRESENTATIONS | Jordan block | DISCRETE-SERIES | GL(N) | symplectic group

Journal Article

American Journal of Mathematics, ISSN 0002-9327, 2018, Volume 140, Issue 6, pp. 1567 - 1638

We describe the supercuspidal representations within certain stable packets, classified by Arthur and Mok using the theory of endoscopy, of a quasi-split unramified unitary group over a p-adic field...

Representations of groups | Cusp forms (Mathematics) | Unitary groups | P-ADIC GROUPS | REDUCIBILITY | MATHEMATICS | K-TYPES | LOCAL LANGLANDS CORRESPONDENCE | SERIES | SUPERCUSPIDAL L-PACKETS | DEPTH | ZERO BASE CHANGE | SEMISIMPLE TYPES | CONJECTURE | Fields, Algebraic | Research | Mathematical research | Group theory | Twisting | Endoscopes | Representations

Representations of groups | Cusp forms (Mathematics) | Unitary groups | P-ADIC GROUPS | REDUCIBILITY | MATHEMATICS | K-TYPES | LOCAL LANGLANDS CORRESPONDENCE | SERIES | SUPERCUSPIDAL L-PACKETS | DEPTH | ZERO BASE CHANGE | SEMISIMPLE TYPES | CONJECTURE | Fields, Algebraic | Research | Mathematical research | Group theory | Twisting | Endoscopes | Representations

Journal Article

Representation Theory of the American Mathematical Society, ISSN 1088-4165, 12/2017, Volume 21, Issue 19, pp. 590 - 610

We establish the unicity of types for depth-zero supercuspidal representations of an arbitrary p-adic group G, showing that each depth-zero supercuspidal representation of G contains a unique...

MATHEMATICS | Langlands correspondence | Theory of types | p-adic groups | depth-zero supercuspidals | MINIMAL K-TYPES

MATHEMATICS | Langlands correspondence | Theory of types | p-adic groups | depth-zero supercuspidals | MINIMAL K-TYPES

Journal Article

Bulletin of the London Mathematical Society, ISSN 0024-6093, 12/2017, Volume 49, Issue 6, pp. 1066 - 1084

.... An irreducible representation of the finite group Gr=GLN(o/pr), for an integer N⩾2, is called regular if its restriction to the principal congruence kernel Kr−1=1+pr−1MN(o/pr...

22E50 (secondary) | 20G25 | 20C15 | 20G05 (primary) | SUPERCUSPIDAL REPRESENTATIONS | MATHEMATICS | GL(N)(O) | CUSPIDAL REPRESENTATIONS | CHARACTERS

22E50 (secondary) | 20G25 | 20C15 | 20G05 (primary) | SUPERCUSPIDAL REPRESENTATIONS | MATHEMATICS | GL(N)(O) | CUSPIDAL REPRESENTATIONS | CHARACTERS

Journal Article

Representation Theory of the American Mathematical Society, ISSN 1088-4165, 09/2019, Volume 23, Issue 8, pp. 249 - 277

.... In this article, we classify \mathfrak{s}-typical representations of K. In particular, we show that the \mathfrak{s}-typical representations of K are precisely the irreducible subrepresentations...

SUPERCUSPIDAL REPRESENTATIONS | Representation theory of p-adic groups | typical representations | theory of types | classical groups | Bernstein decomposition | HECKE ALGEBRAS | inertial equivalence | PRINCIPAL SERIES | SEMISIMPLE TYPES | MATHEMATICS | UNICITY | depth-zero inertial classes

SUPERCUSPIDAL REPRESENTATIONS | Representation theory of p-adic groups | typical representations | theory of types | classical groups | Bernstein decomposition | HECKE ALGEBRAS | inertial equivalence | PRINCIPAL SERIES | SEMISIMPLE TYPES | MATHEMATICS | UNICITY | depth-zero inertial classes

Journal Article

Journal of Number Theory, ISSN 0022-314X, 12/2015, Volume 157, pp. 280 - 290

Let F be a local non-archimedean field of characteristic zero. We provide a classification of the irreducible, generic representations of GL(n,F...

Generic representation | Distinguished representation | Parabolic induction | MATHEMATICS | TAME SUPERCUSPIDAL REPRESENTATIONS

Generic representation | Distinguished representation | Parabolic induction | MATHEMATICS | TAME SUPERCUSPIDAL REPRESENTATIONS

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 12/2019, Volume 50, Issue 3, pp. 589 - 619

Let $$\pi $$ π be a simple supercuspidal representation of the symplectic group $${\mathrm {Sp}}_{2l}(F)$$ Sp 2 l ( F ) , over a p-adic field F...

Secondary 11F85 | Functions of a Complex Variable | Field Theory and Polynomials | Mathematics | Local Langlands conjecture | Rankin–Selberg method | Simple supercuspidal | Primary 11S37 | Fourier Analysis | 22E50 | Number Theory | Combinatorics | 22E55

Secondary 11F85 | Functions of a Complex Variable | Field Theory and Polynomials | Mathematics | Local Langlands conjecture | Rankin–Selberg method | Simple supercuspidal | Primary 11S37 | Fourier Analysis | 22E50 | Number Theory | Combinatorics | 22E55

Journal Article

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