Double Affine Hecke Algebras and Their Applications by Etingof, Pavel I

“…I will talk about double affine Hecke algebras and their applications.…”
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Cyclotomic double affine Hecke algebras by Alexander BRAVERMAN, Pavel ETINGOF, Michael FINKELBERG

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Cocenters and representations of affine Hecke algebras by Ciubotaru, D, He, X

“…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 between the rigid cocenter, an important subspace of the cocenter, and the dual object in representation theory, the rigid quotient of the Grothendieck group of finite-dimensional representations.…”

Star operations for affine Hecke algebras by Barbasch, D, Ciubotaru, D

“…In this paper, we consider the star operations for (graded) affine Hecke algebras which preserve certain natural filtrations. …”

Double affine Hecke algebras and noncommutative geometry by Oblomkov, Alexei

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Crystals and affine Hecke algebras of type D by Kashiwara, M, Miemietz, V

“…Enomoto and the first author presented the notion of symmetric crystals and formulated analogous conjectures for the affine Hecke algebras of type B. In this note, we present similar conjectures for certain classes of irreducible representations of affine Hecke algebras of type D. …”

A Coherent Categorification of the Asymptotic Affine Hecke Algebra by Propp, Oron Yehonatan

“…Kazhdan–Lusztig categorified the affine Hecke algebra H in terms of equivariant coherent sheaves on the Steinberg variety. …”
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On representation theory of affine Hecke algebras of type B by Miemietz, V

“…Ariki's and Grojnowski's approach to the representation theory of affine Hecke algebras of type $A$ is applied to type $B$ with unequal parameters to obtain -- under certain restrictions on the eigenvalues of the lattice operators -- analogous multiplicity-one results and a classification of irreducibles with partial branching rules as in type $A$.…”

Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras by Dodd, Christopher Stephen

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A uniform classification of discrete series representations of affine Hecke algebras by Ciubotaru, D, Opdam, E

“…This classification applies to all semisimple affine Hecke algebras H, and to all v 2 Q, where Q denotes the vector group of positive real (possibly unequal) Hecke parameters for H. …”

Affine Hecke algebras, canonical bases and a derived Deligne-Langlands correspondence by Antor, J

“…<p>This thesis makes several contributions to the representation theory of affine Hecke algebras and related topics:</p> <p>• We show that there is an equivalence of triangulated categories relating certain (dg-)modules over affine Hecke algebras with certain categories of constructible sheaves. …”

On the reducibility of induced representations for classical p-adic groups and related affine Hecke algebras by Ciubotaru, D, Heiermann, V

“…More generally, we study, for a given set I of inertial orbits of supercuspidal representations of p-adic general linear groups, the category CI,σ of smooth complex finitely generated representations of classical p-adic groups of fixed type, but arbitrary rank, and supercuspidal support given by σ and I, show that this category is equivalent to a category of finitely generated right modules over a direct sum of tensor products of extended affine Hecke algebras of type A, B and D and establish functoriality properties, relating categories with disjoint I’s. …”

ℤ/����ℤ-graded Lie algebras and perverse sheaves, III: Graded double affine Hecke algebra by Lusztig, George, Yun, Zhiwei

“…In this paper we construct representations of certain graded double affine Hecke algebras (DAHA) with possibly unequal parameters from geometry. …”
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A Lie-theoretic construction of some representations of the degenerate affine and double affine Hecke algebras of type BCn by Etingof, Pavel I., Freund, Rebecca L., Ma, Xiaoguang

“…We construct a functor from the category of Harish-Chandra modules for the pair (G,K) to the category of representations of the degenerate affine Hecke algebra of type B_n [B subscript n], and a functor from the category of K-monodromic twisted D-modules on G/K to the category of representations of the degenerate double affine Hecke algebra of type BC_n [BC subscript n]; the second functor is an extension of the first one.…”
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On the structure of the affine asymptotic Hecke algebras by BEZRUKAVNIKOV, ROMAN, DAWYDIAK, STEFAN, DOBROVOLSKA, GALYNA

“…We also show that Lusztig's homomorphism from the affine Hecke algebra to the asymptotic affine Hecke algebra induces an isomorphism on cocenters and discuss the relation of the above central extensions to the structure of the cocenter.…”
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On the centre of the cyclotomic Hecke algebras of $G(m,1,2)$ by McGerty, K

“…We compute the centre of the cyclotomic Hecke algebra attached to $G(m,1,2)$ and show that if $q \neq 1$ it is equal to the image of the centre of the affine Hecke algebra $\Ha$. We also briefly discuss what is known about the relation between the centre of an arbitrary cyclotomic Hecke algebra and the centre of the affine Hecke algebra of type $A$.…”

Towards a functor between affine and finite Hecke categories in type A by Tolmachov, Kostiantyn

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On trigonometric and elliptic Cherednik algebras by Ma, Xiaoguang, Ph. D. Massachusetts Institute of Technology

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Affine braid group actions on derived categories of springer resolutions by Bezrukavnikov, Roman, Richie, Simon

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Algorithm for Iwahori-Matsumoto duality for tempered unipotent representations of geometric Hecke algebras of type B, C, D by La, R

“…The Iwahori–Matsumoto involution is an involutive operation on the Grothendieck group of complex finite-dimensional representations of an affine Hecke algebra, or a graded Hecke algebra. The Aubert–Zelevinsky involution is another involutive operation on the Grothendieck group of complex finite-length representations of <em>p</em>-adic groups. …”