2017, Contemporary mathematics, ISBN 9781470424602, Volume 683., x, 361 pages

Book

Advances in Mathematics, ISSN 0001-8708, 04/2017, Volume 311, pp. 662 - 729

We prove that cyclotomic Yokonuma–Hecke algebras of type A are cyclotomic quiver Hecke algebras and we give an explicit isomorphism with its inverse, using a similar result of Brundan and Kleshchev on cyclotomic Hecke algebras...

Yokonuma–Hecke algebra | Representation theory | Quiver Hecke algebra | MATHEMATICS | Yokonuma-Hecke algebra | DECOMPOSITION NUMBERS | Algebra | Mathematics - Representation Theory | Mathematics | Representation Theory

Yokonuma–Hecke algebra | Representation theory | Quiver Hecke algebra | MATHEMATICS | Yokonuma-Hecke algebra | DECOMPOSITION NUMBERS | Algebra | Mathematics - Representation Theory | Mathematics | Representation Theory

Journal Article

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 subalgebra of g...

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

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

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...

Affine Hecke algebras | Cyclotomic Hecke algebras | Quiver Hecke algebras | MATHEMATICS | BLOCKS | IDEMPOTENTS | Algebra

Affine Hecke algebras | Cyclotomic Hecke algebras | Quiver Hecke algebras | MATHEMATICS | BLOCKS | IDEMPOTENTS | Algebra

Journal Article

2008, Mathematical surveys and monographs, ISBN 9780821841860, Volume no. 150., xxv, 759

Book

Algebra Colloquium, ISSN 1005-3867, 2012, Volume 19, Issue 2, pp. 359 - 410

We provide an introduction to the 2-representation theory of Kac-Moody algebras, starting with basic properties of nil Hecke algebras and quiver Hecke algebras, and continuing with the resulting...

Hecke algebras | representations | quiver varieties | Lie algebras | MATHEMATICS | MATHEMATICS, APPLIED | QUANTUM SL | SHEAVES | ARTIN STACKS

Hecke algebras | representations | quiver varieties | Lie algebras | MATHEMATICS | MATHEMATICS, APPLIED | QUANTUM SL | SHEAVES | ARTIN STACKS

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 2018, Volume 51, Issue 1, pp. 51 - 88

We prove that the class of Brauer graph algebras coincides with the class of indecomposable idempotent algebras of biserial weighted surface algebras...

Periodic algebra | Tame algebra | Weighted surface algebra | Biserial weighted surface algebra | Quiver combinatorics | Brauer graph algebra | Symmetric algebra | Special biserial algebra | HECKE ALGEBRAS | MATHEMATICS | REPRESENTATION TYPE | MODULES | BLOCKS

Periodic algebra | Tame algebra | Weighted surface algebra | Biserial weighted surface algebra | Quiver combinatorics | Brauer graph algebra | Symmetric algebra | Special biserial algebra | HECKE ALGEBRAS | MATHEMATICS | REPRESENTATION TYPE | MODULES | BLOCKS

Journal Article

Algebras and representation theory, ISSN 1572-9079, 2019, Volume 23, Issue 3, pp. 1177 - 1196

In Jensen and Su (J. Pure Appl. Algebra 219(2), 277-307 2014) constructed 0-Schur algebras, using double flag varieties...

Nil-Temperley-Lieb algebras | MATHEMATICS | Double flag varieties | 0-Schur algebras | Nil-Hecke algebras | HECKE ALGEBRAS | Quivers

Nil-Temperley-Lieb algebras | MATHEMATICS | Double flag varieties | 0-Schur algebras | Nil-Hecke algebras | HECKE ALGEBRAS | Quivers

Journal Article

Algebras and representation theory, ISSN 1572-9079, 2019, Volume 23, Issue 3, pp. 759 - 794

This paper is investigative work into the properties of a family of graded algebras recently defined by Varagnolo and Vasserot, which we call VV algebras...

MATHEMATICS | Morita equivalence | Affine cellularity | KLR algebras | Affine quasi-heredity | HECKE ALGEBRAS | AFFINE | VV algebras

MATHEMATICS | Morita equivalence | Affine cellularity | KLR algebras | Affine quasi-heredity | HECKE ALGEBRAS | AFFINE | VV algebras

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 02/2014, Volume 163, Issue 3, pp. 619 - 663

.... In particular, every PBW basis of such quantum groups is proven to yield a semi-orthogonal collection in the module category of the Khovanov-Lauda-Rouquier (KLR) algebras...

MATHEMATICS | HECKE ALGEBRAS | UNIVERSAL ENVELOPING-ALGEBRAS | QUANTUM GROUPS | 17B37 | 16T20

MATHEMATICS | HECKE ALGEBRAS | UNIVERSAL ENVELOPING-ALGEBRAS | QUANTUM GROUPS | 17B37 | 16T20

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2019, Volume 371, Issue 10, pp. 6883 - 6902

We define a class of algebras which are distinguished by a PBW property and an orthogonality condition, and which we call Hopf-Hecke algebras , since they generalize the Drinfeld Hecke algebras...

MATHEMATICS | HECKE ALGEBRAS | REPRESENTATIONS | OPERATOR | DEFORMATIONS

MATHEMATICS | HECKE ALGEBRAS | REPRESENTATIONS | OPERATOR | DEFORMATIONS

Journal Article

International journal of mathematics, ISSN 1793-6519, 2019, Volume 30, Issue 1, p. 1950002

Let [Formula: see text] be the Lusztig integral form of quantum [Formula: see text]. There is a natural surjective algebra homomorphism...

quantum n | Hecke algebras | Quantum Schur algebras | MATHEMATICS | quantum gl(n) | BASES | Algebra

quantum n | Hecke algebras | Quantum Schur algebras | MATHEMATICS | quantum gl(n) | BASES | Algebra

Journal Article

Advances in Mathematics, ISSN 0001-8708, 11/2016, Volume 303, pp. 1122 - 1161

In this article we study in detail the category of noncommutative motives of separable algebras Sep(k...

Separable algebra | dg Azumaya algebra | Hecke algebra | Convolution | Noncommutative motives | Brauer group | Cyclic sieving phenomenon | Twisted flag variety | VARIETIES | CATEGORIES | ADDITIVE INVARIANTS | EQUIVALENCE | AZUMAYA ALGEBRAS | MATHEMATICS | NUMERICAL MOTIVES | Aluminum compounds | Usage | Algebra | Analysis

Separable algebra | dg Azumaya algebra | Hecke algebra | Convolution | Noncommutative motives | Brauer group | Cyclic sieving phenomenon | Twisted flag variety | VARIETIES | CATEGORIES | ADDITIVE INVARIANTS | EQUIVALENCE | AZUMAYA ALGEBRAS | MATHEMATICS | NUMERICAL MOTIVES | Aluminum compounds | Usage | Algebra | Analysis

Journal Article

Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 08/2017, Volume 26, Issue 9, p. 1743005

...–Hecke algebras Y d , n ( q ) , which are not topologically equivalent to the Homflypt polynomial...

framization | Yokonuma-Hecke algebra | Temperley-Lieb algebra | link invariants | MATHEMATICS | REPRESENTATIONS | ADIC FRAMED BRAIDS | KNOTS | Algebra

framization | Yokonuma-Hecke algebra | Temperley-Lieb algebra | link invariants | MATHEMATICS | REPRESENTATIONS | ADIC FRAMED BRAIDS | KNOTS | Algebra

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 2/2017, Volume 20, Issue 1, pp. 71 - 121

We construct analogues for the Brauer, BMW, partition, and Jones–Temperley–Lieb algebras of the Murphy basis of the Hecke algebra of the symmetric group...

Jones basic construction | Associative Rings and Algebras | 05E10 | Partition algebra | Cellular algebra | Non-associative Rings and Algebras | Murphy basis | Commutative Rings and Algebras | 20G05 | Mathematics | Brauer algebra | Birman–Murakami–Wenzl algebra | REPRESENTATIONS | FORM | HECKE ALGEBRAS | Birman-Murakami-Wenzl algebra | PARTITION ALGEBRAS | MATHEMATICS | SEMISIMPLICITY CRITERIA | BRAUER | MURAKAMI-WENZL ALGEBRAS | GRAM DETERMINANTS | Algebra

Jones basic construction | Associative Rings and Algebras | 05E10 | Partition algebra | Cellular algebra | Non-associative Rings and Algebras | Murphy basis | Commutative Rings and Algebras | 20G05 | Mathematics | Brauer algebra | Birman–Murakami–Wenzl algebra | REPRESENTATIONS | FORM | HECKE ALGEBRAS | Birman-Murakami-Wenzl algebra | PARTITION ALGEBRAS | MATHEMATICS | SEMISIMPLICITY CRITERIA | BRAUER | MURAKAMI-WENZL ALGEBRAS | GRAM DETERMINANTS | Algebra

Journal Article

Journal of Algebra, ISSN 0021-8693, 04/2017, Volume 476, pp. 85 - 112

...) of the degenerate affine Hecke–Clifford and spin Hecke algebras in classical types.

Spin representation theory | Cocenter | Degenerate affine Hecke–Clifford algebras | Degenerate affine spin Hecke algebras | MATHEMATICS | Degenerate affine Hecke-Clifford algebras | Algebra | Mathematics - Representation Theory

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

Algebras and Representation Theory, ISSN 1386-923X, 8/2012, Volume 15, Issue 4, pp. 675 - 696

Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras $\bigoplus_{n\ge0}A_n...

Grothendieck group | Associative Rings and Algebras | Dual graded graphs | Non-associative Rings and Algebras | Grothendieck groups 18F30 | Hopf algebras 16W30 | Commutative Rings and Algebras | Mathematics | Graded algebra | Hopf algebra | MATHEMATICS | BASES | HECKE ALGEBRAS | SYMMETRICAL FUNCTIONS | CATEGORIES | Algebra | Universities and colleges

Grothendieck group | Associative Rings and Algebras | Dual graded graphs | Non-associative Rings and Algebras | Grothendieck groups 18F30 | Hopf algebras 16W30 | Commutative Rings and Algebras | Mathematics | Graded algebra | Hopf algebra | MATHEMATICS | BASES | HECKE ALGEBRAS | SYMMETRICAL FUNCTIONS | CATEGORIES | Algebra | Universities and colleges

Journal Article

Duke mathematical journal, ISSN 0012-7094, 2017, Volume 166, Issue 6, pp. 1005 - 1101

.... It is a Rees algebra associated with the center of cyclotomic degenerate affine Hecke algebras of type...

MATHEMATICS | DUALITY | COHOMOLOGY | LAUDA-ROUQUIER ALGEBRAS | QUANTUM GROUPS | WEYL MODULES | Mathematics - Representation Theory

MATHEMATICS | DUALITY | COHOMOLOGY | LAUDA-ROUQUIER ALGEBRAS | QUANTUM GROUPS | WEYL MODULES | Mathematics - Representation Theory

Journal Article

2005, London Mathematical Society lecture note series, ISBN 0521609186, Volume 319, xii, 434

.... It is a major source of general information about the double affine Hecke algebra, also called Cherednik's algebra, and its impressive applications...

Harmonic analysis | Hecke algebras | Affine algebraic groups | Knizhnik-Zamolodchikov equations | Orthogonal polynomials | Knizhnik-Zamoldchikov equations

Harmonic analysis | Hecke algebras | Affine algebraic groups | Knizhnik-Zamolodchikov equations | Orthogonal polynomials | Knizhnik-Zamoldchikov equations

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