Questions tagged [affine-hecke-algebras]

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Parabolic induction, and tensoring (Iwahori/affine) Hecke algebras

In several places, such as [1] and [2], it seems to be implicitly known that (normalized) parabolic induction corresponds to tensoring affine Hecke algebras. I say implicitly because both [1] and [2] ...
Kristaps John Balodis's user avatar
5 votes
0 answers

Is there a derived version of affine Schur-Weyl duality?

One version of affine Schur-Weyl duality states that there is a fully faithful functor from representation of $A_r$ affine Hecke algebra to the representation of $A_n$ affine Lie group assuming $r<...
Xu Kai's user avatar
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4 votes
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Gelfand's transform for noncommutative $C^*$-algebras

Please excuse me if this is well-known, I am not very familiar with the general theory of $C^*$-algebras. Let $A$ be a unital separable liminal $C^*$-algebra (in the case I am interested in, ...
Antoine Labelle's user avatar
5 votes
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p-adic Hecke operators in the Iwahori-Hecke algebra $C_c(J\backslash G(F)/J)$

$\DeclareMathOperator\ch{ch}$Let $F$ be a non-archimedean local field, $\mathcal{O}$ its ring of integers, $\mathfrak{p}$ its maximal ideal and $\pi$ a uniformizer. I shall use $\kappa(F)$ to denote ...
Maty Mangoo's user avatar
4 votes
0 answers

Towers of algebras, their 2-step centralizer algebras, and analogues of the degenerate affine Hecke algebra

Let $\, \big( {\frak{F}}_0 \subset {\frak{F}}_1 \subset {\frak{F}}_2 \subset \cdots \big)$ be a tower of semi-simple, finite dimensional, unital, complex algebras starting with ${\frak{F}}_0 \cong \...
Jeanne Scott's user avatar
  • 1,767
4 votes
1 answer

A problem on Kazhdan–Lusztig theorem

I am reading Chriss, Ginzburg's book Representation theory and complex geometry. In theorem 7.2.16 it says that the convolution action of the Steinberg variety $St=\tilde{\mathcal{N}}\times_\mathfrak{...
Yang's user avatar
  • 71
1 vote
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Coincidence of notation in the classification of representations of affine Hecke algebras

This is spurred by a short discussion I had in the comments of this MO question. In Ginzburg's 1998 paper,, or equivalently in the book by Chriss and Ginzburg, &...
mi.f.zh's user avatar
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1 vote
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Block sum for degenerate affine Hecke algebras

The degenerate affine Hecke algebra $H_k$ over a field $F$ is the algebra with generators $s_1,\ldots,s_{k-1}$ and $x_1,\ldots,x_k$, subject to the following relations: $s_is_js_i=s_js_is_j$ for $i=j\...
Richard Hepworth's user avatar
4 votes
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Kazhdan-Lusztig basis elements appearing in product with distinguished involution

My apologies if the below is too malformed to make sense. Let $(W,S)$ be the affine Weyl group of a reductive group $G$, and let $\{C_w\}$ be the Kazhdan-Lusztig $C$-basis (an answer in terms of the $...
Stefan  Dawydiak's user avatar
1 vote
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Coefficient ring of Satake isomorphism

Let $G$ be a split reductive group over local field $F$, $G^L$ be the (complex) Langlands dual group of $G$. Denote $H$ to be the $\mathbb{Z}$-Hecke algebra of $G$, that is the ring of $G(\mathcal{O}...
userabc's user avatar
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7 votes
1 answer

Geometric interpretations of nil-Hecke ring and affine Hecke algebra

I am interested in two related constructions which give us either the cohomology or the $T \times \mathbb{C}^*$-equivariant $K$-theory of flag varieties. Let $G$ be a semisimple, simply connected ...
Marc Besson's user avatar
8 votes
1 answer

Affine vs Yokonuma

Let $G=GL_n$. Let us start with the Hecke algebra $H_n$. It acts on K(constructible sheaves on $G/B$) by Hecke correpondences and on K(coherent sheaves on $G/B$) by Lusztig's construction [1]. Now we ...
Anton Mellit's user avatar
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8 votes
2 answers

Relation between representations of p-adic groups and affine Hecke algebras

Let $R_n$ be the category of complex-valued smooth finite-length representations of the group $GL_n(F)$, where $F$ is a local field. By the result of Borel, the subcategory of $R_n$ consisting of ...
Jianrong Li's user avatar
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