Related papers: Cellular structures on Hecke algebras of type B
The level l Fock space admits canonical bases G_e and G_\infty. They correspond to U_{v}(hat{sl}_{e}) and U_{v}(sl_{\infty})-module structures. We establish that the transition matrices relating these two bases are unitriangular with…
We give an equivalence of categories between certain subcategories of modules of pro-$p$-Iwahori Hecke algebras and modulo $p$ representations.
In this paper, we discuss the theory of the Siegel modular variety in the aspects of arithmetic and geometry. This article covers the theory of Siegel modular forms, the Hecke theory, a lifting of elliptic cusp forms, geometric properties…
In this paper we study spaces of algebras over an operad (non-symmetric) in symmetric monoidal model categories. We first compute the homotopy fiber of the forgetful functor sending an algebra to its underlying object, extending a result of…
We show that the category O for a rational Cherednik algebra of type A is equivalent to modules over a q-Schur algebra (parameter not a half integer), providing thus character formulas for simple modules. We give some generalization to…
In this paper, we look at the problem of determining the composition factors for the affine graded Hecke algebra via the computation of Kazhdan-Lusztig type polynomials. We review the algorithms of \cite{L1,L2}, and use them in particular…
The Lascoux-Leclerc-Thibon-Ariki theory asserts that the K-group of the representations of the affine Hecke algebras of type A is isomorphic to the algebra of functions on the maximal unipotent subgroup of the group associated with a Lie…
We discuss selected topics on the topology of moduli spaces of curves and maps, emphasizing their relation with Gromov--Witten theory and integrable systems.
The relative cell complexes with respect to a generating set of cofibrations are an important class of morphisms in any model structure. In the particular case of the standard (algebraic) model structure on $\textbf{Top}$, we give a new…
We show that an adaptation of Landrock's Lemma for symmetric algebras also holds for cellular algebras and BGG algebras. This is a result relating the radical layers of any two projective modules. The reason it holds in our setting is that…
We show that coefficients in unicellular LLT polynomials are evaluations of Hecke algebra traces at Kazhdan-Lusztig basis elements. We express these in terms of traditional trace bases, induction, and Kazhdan-Lusztig R-polynomials.
We construct a family of exact functors from the BGG category of representations of the Lie algebra sl to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke algebra H of GL. These functors…
We construct a combinatorial moduli space closely related to the KSV-compactification of the moduli space of bordered marked Riemann surfaces. The open part arises from symmetric metric ribbon graphs. The compactification is obtained by…
We introduce the combinatorial model of $J$-folded alcove paths in an affine Weyl group and construct representations of affine Hecke algebras using this model. We study boundedness of these representations, and we state conjectures linking…
The paper aims to introduce the cyclotomic $q$-Schur superalgebra via the permutation supermodules of the cyclotomic Hekce algebra and investigate its structure. In particular, we show that the cyclotomic $q$-Schur superalgebra is a…
We study the representation theory of the type B Schur algebra $\mathcal{L}^n(m)$ with unequal parameters introduced in work of Lai, Nakano and Xiang. For generic values of $q,Q$, this algebra is semi-simple and Morita equivalent to the…
Hecke algebras are usually defined algebraically, via generators and relations. We give a new algebro-geometric construction of affine and double-affine Hecke algebras (the former is known as the Iwahori-Hecke algebra, and the latter was…
We introduce and study an affine analogue of skew Young diagrams and tableaux on them. It turns out that the double affine Hecke algebra of type $A$ acts on the space spanned by standard tableaux on each diagram. It is shown that the…
Let $G$ be a general linear group over a $p$-adic field. It is well known that Bernstein components of the category of smooth representations of $G$ are described by Hecke algebras arising from Bushnell-Kutzko types. We describe the…
We define canonical bases of the higher-level q-deformed Fock space modules of the affine Lie algebra sl(n)^. This generalizes the result of Leclerc and Thibon for the case of level 1. We express the transition matrices between the…