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Journal of Algebra, ISSN 0021-8693, 04/2017, Volume 476, pp. 85 - 112
We determine a basis of the cocenter (i.e., the trace or zeroth Hochschild homology) of the degenerate affine Hecke–Clifford and spin Hecke algebras in... 
Spin representation theory | Cocenter | Degenerate affine Hecke–Clifford algebras | Degenerate affine spin Hecke algebras | MATHEMATICS | Degenerate affine Hecke-Clifford algebras | Algebra | Mathematics - Representation Theory
Journal Article
2017, Contemporary mathematics, ISBN 9781470424602, Volume 683., x, 361 pages
Book
Duke Mathematical Journal, ISSN 0012-7094, 2015, Volume 164, Issue 8, pp. 1549 - 1602
Let g be an untwisted affine Kac-Moody algebra of type A(n)((1)) (n >= 0 or D-n((1)) (n >= 4), and let g(0) be the underlying finite-dimensional simple Lie... 
MATHEMATICS | BASES | DUAL CANONICAL BASIS | Q-CHARACTERS | VARIETIES | FINITE-DIMENSIONAL REPRESENTATIONS | CLUSTER ALGEBRAS | LAUDA-ROUQUIER ALGEBRAS | EXCITATION-SPECTRA | Mathematics - Representation Theory | quiver Hecke algebra | quantum group | 16G | 81R50 | quantum affine algebra | 17B37 | 16T25
Journal Article
by Hu, Jun and Li, Fang
Journal of Algebra, ISSN 0021-8693, 01/2020, Volume 541, pp. 219 - 269
We introduce some modified forms for the degenerate and non-degenerate affine Hecke algebras of type A. These are certain subalgebras living inside the inverse... 
Affine Hecke algebras | Cyclotomic Hecke algebras | Quiver Hecke algebras | MATHEMATICS | BLOCKS | IDEMPOTENTS | Algebra
Journal Article
Journal of Algebra, ISSN 0021-8693, 02/2018, Volume 496, pp. 292 - 314
We establish an explicit algebra isomorphism between the affine Yokonuma–Hecke algebra Yˆr,n(q) and a direct sum of matrix algebras with coefficients in tensor... 
Matrix algebras | Global dimension | Affine cellular algebras | Affine Yokonuma–Hecke algebras | MATHEMATICS | 2-SIDED CELLS | Affine Yokonuma-Hecke algebras | Algebra
Journal Article
Mathematical Research Letters, ISSN 1073-2780, 2016, Volume 23, Issue 3, pp. 707 - 718
We prove that the affine Yokonuma-Hecke algebra defined by Chlouveraki and Poulain d'Andecy is a particular case of the pro-p-Iwahori-Hecke algebra defined by... 
Yokonuma-Hecke algebras | Affine Hecke algebras | Affine Yokonuma-Hecke algebras | Pro-p-Iwahori-Hecke algebras | pro-p-Iwahori-Hecke algebras | MATHEMATICS | affine Hecke algebras | affine Yokonuma-Hecke algebras
Journal Article
2005, London Mathematical Society lecture note series, ISBN 0521609186, Volume 319, xii, 434
This is an essentially self-contained monograph in an intriguing field of fundamental importance for Representation Theory, Harmonic Analysis, Mathematical... 
Harmonic analysis | Hecke algebras | Affine algebraic groups | Knizhnik-Zamolodchikov equations | Orthogonal polynomials | Knizhnik-Zamoldchikov equations
Book
Advances in Mathematics, ISSN 0001-8708, 07/2014, Volume 259, pp. 134 - 172
We develop an inductive approach to the representation theory of the Yokonuma–Hecke algebra Yd,n(q), based on the study of the spectrum of its Jucys–Murphy... 
Yokonuma–Hecke algebra | Jucys–Murphy elements | Partitions | Affine Yokonuma–Hecke algebra | Schur elements | Standard tableaux | Representations | Affine Yokonuma-Hecke algebra | Jucys-Murphy elements | Yokonuma-Hecke algebra | MATHEMATICS | COMPLEX REFLECTION GROUPS | ADIC FRAMED BRAIDS | Analysis | Algebra | Mathematics
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 02/2019, Volume 136, pp. 268 - 283
We consider the Hecke pair consisting of the group PK+ of affine transformations of a number field K that preserve the orientation in every real embedding and... 
Ground state | Groupoid | Hecke algebra | KMS-state | Bost–Connes system | CONNES | PHYSICS, MATHEMATICAL | TOEPLITZ ALGEBRA | AFFINE SEMIGROUP | MATHEMATICS | KMS STATES | Bost-Connes system | PART | SYSTEMS
Journal Article
Journal of the Institute of Mathematics of Jussieu, ISSN 1474-7480, 10/2015, Volume 14, Issue 4, pp. 837 - 855
We study the action of the formal affine Hecke algebra on the formal group algebra, and show that the the formal affine Hecke algebra has a basis indexed by... 
formal group law | formal group algebra | affine Hecke algebra | SURGERY | INVARIANTS | ORIENTED COHOMOLOGY | FLAGS | Algebraic group theory | Generators | Algebra | Mathematical analysis | Modules | Group theory
Journal Article
Compositio Mathematica, ISSN 0010-437X, 07/2016, Volume 152, Issue 7, pp. 1333 - 1384
In this paper we propose and discuss implications of a general conjecture that there is a natural action of a rank 1 double affine Hecke algebra on the... 
quantum torus | skein modules | character variety | Kauffman bracket | double affine Hecke algebras | knots | Jones polynomial | COMPLEX REFLECTION GROUPS | REPRESENTATIONS | RESHETIKHIN-TURAEV | KNOT | BRACKET SKEIN MODULE | MATHEMATICS | QUASI-INVARIANTS | CHARACTER VARIETIES | 3-MANIFOLDS | ASYMPTOTICS | WITTEN | Polynomials | Algebra | Skeins | Modules | Complement | Recursion | Invariants | Knots
Journal Article
Advances in Mathematics, ISSN 0001-8708, 2007, Volume 216, Issue 2, pp. 854 - 878
This paper classifies the blocks of the cyclotomic Hecke algebras of type G ( r , 1 , n ) over an arbitrary field. Rather than working with the Hecke algebras... 
Cyclotomic Schur algebras | Blocks | Affine Hecke algebras | Cyclotomic Hecke algebras | MATHEMATICS | cyclotomic hecke algebras | cyclotomic schur algebras | affine hecke algebras | blocks
Journal Article
Advances in Mathematics, ISSN 0001-8708, 09/2015, Volume 282, pp. 23 - 46
The quantum loop algebra of gl n is the affine analogue of quantum gl n . In the seminal work [1], Beilinson-Lusztig-MacPherson gave a beautiful realisation... 
Ringel-Hall algebras | The quantum loop algebra of gl n | Affine quantum Schur algebras | Employee motivation | Algebra
Journal Article
Advances in Mathematics, ISSN 0001-8708, 01/2016, Volume 286, pp. 912 - 957
We introduce the notion of spectral transfer morphisms between normalized affine Hecke algebras, and show that such morphisms induce spectral measure... 
Plancherel measure | Affine Hecke algebra | Secondary | Primary | P-ADIC GROUPS | FORMAL DEGREES | MATHEMATICS | DISCRETE-SERIES | REPRESENTATIONS | DECOMPOSITION | L-PACKETS | CHARACTERS | Algebra
Journal Article
Advances in Mathematics, ISSN 0001-8708, 09/2014, Volume 262, pp. 370 - 435
We give a proof of the parabolic/singular Koszul duality for the category O of affine Kac–Moody algebras. The main new tool is a relation between moment graphs... 
Affine Kac–Moody algebras | Koszul duality | Cherednik algebras | Affine Kac-Moody algebras | MATHEMATICS | LOCALIZATION | FUNCTORS | CATEGORY | MOMENT GRAPHS | TRANSLATION | Algebra
Journal Article
Journal of Algebra, ISSN 0021-8693, 04/2016, Volume 452, pp. 502 - 548
Class polynomials attached to affine Hecke algebras were first introduced by He in [13]. They play an important role in the study of affine Deligne–Lusztig... 
Affine Weyl group | Class polynomial | Affine Deligne–Lusztig variety | Affine Hecke algebra | Affine Deligne-Lusztig variety | MATHEMATICS | DIMENSIONS | ELEMENTS | DELIGNE-LUSZTIG VARIETIES | FLAG VARIETIES | Algebra
Journal Article
Journal of the European Mathematical Society, ISSN 1435-9855, 2017, Volume 19, Issue 10, pp. 3143 - 3177
In this paper, we study the relationship between the cocenter and the representation theory of affine Hecke algebras. The approach is based on the interaction... 
Trace Paley-Wiener theorem | Cocenter | Affine Hecke algebra | Density theorem | P-ADIC GROUPS | MATHEMATICS | MATHEMATICS, APPLIED | ADDITIONAL STRUCTURE | WEYL GROUPS | SERIES | density theorem | ISOCRYSTALS | trace Paley-Wiener theorem | cocenter | CHARACTERS
Journal Article
Representation Theory of the American Mathematical Society, ISSN 1088-4165, 06/2017, Volume 21, Issue 6, pp. 82 - 105
In this paper, we study the relation between the cocenter \overline {{\tilde {\mathcal H}}} and the representations of an affine pro- p Hecke algebra {\tilde... 
Hecke algebras | P-adic groups | Affine Coxeter groups | MATHEMATICS | MODULES | p-adic groups | PARABOLIC INDUCTION | MINIMAL LENGTH ELEMENTS | FINITE COXETER GROUPS | ADIC GROUP | CHARACTERS
Journal Article
Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 02/2016, Volume 2016, Issue 711, pp. 1 - 54
We introduce a new family of superalgebras which should be considered as a super version of the Khovanov–Lauda–Rouquier algebras. Let be the set of vertices of... 
PROJECTIVE-REPRESENTATIONS | MATHEMATICS | CRYSTAL BASES | QUANTUM AFFINE ALGEBRAS | YOUNG SYMMETRIZERS
Journal Article
Advances in Mathematics, ISSN 0001-8708, 09/2017, Volume 317, pp. 50 - 90
For any formal group law, there is a formal affine Hecke algebra defined by Hoffnung–Malagón-López–Savage–Zainoulline. Coming from this formal group law, there... 
Formal group law | Oriented cohomology theory | Springer fiber | Affine Hecke algebra | MATHEMATICS | INVARIANTS | EQUIVARIANT K-THEORY | ORIENTED COHOMOLOGY | Algebra
Journal Article
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