Related papers: On decomposition numbers of the cyclotomic q-Schur…
For the Schur superalgebra $S=S(m|n,r)$ over a ground field $K$ of characteristic zero, we define symmetrizers $T^{\lambda}[i:j]$ of the ordered pairs of tableaux $T_i, T_j$ of the shape $\lambda$ and show that the $K$-span $A_{\lambda,K}$…
This work introduces a novel $q$-$\hbar$ deformation of the Heisenberg algebra, designed to unify and extend several existing $q$-deformed formulations. Starting from the canonical Heisenberg algebra defined by the commutation relation…
Let $X$ be a normal geometrically connected variety over a finite field $\kappa$ of characteristic~$p$. Let $E$ be a number field. Using automorphic methods over global function fields, we derive properties of the geometric monodromy groups…
In this paper we prove the following results: $1)$ We show that any arithmetic quotient of a homogeneous space admits a natural real semi-algebraic structure for which its Hecke correspondences are semi-algebraic. A particularly important…
We define an integral form of the deformed W-algebra of type gl_r, and construct its action on the K-theory groups of moduli spaces of rank r stable sheaves on a smooth projective surface S, under certain assumptions. Our construction…
We investigate the representation theory of certain specializations of the Ariki-Koike algebras, obtained by setting $q=0$ in a suitably normalized version of Shoji's presentation. We classify the simple and projective modules, and describe…
Motivated by the group entropy theory, in this work we generalize the algebra of real numbers (that we called G-algebra), from which we develop an associated G-differential calculus. Thus, the algebraic structures corresponding to the…
Let $V$ be a finite dimensional vector space. Given a decomposition $V\otimes V=\oplus_i^n I_i$, define $n$ quadratic algebras $(V, J_m)$ where $J_m=\oplus_{i\neq m} I_i$. This decomposition defines also the quantum semigroup…
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 limit of cyclotomic Hecke algebras. We construct faithful representations and…
We initiate a study of Hilbert modules over the polynomial algebra A=C[z_1,...,z_d] that are obtained by completing A with respect to an inner product having certain natural properties. A standard Hilbert module is a finite multiplicity…
We construct an explicit isomorphism between (truncations of) quiver Hecke algebras and Elias-Williamson's diagrammatic endomorphism algebras of Bott-Samelson bimodules. As a corollary, we deduce that the decomposition numbers of these…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
A Lie conformal algebra is an algebraic structure that encodes the singular part of the operator product expansion of chiral fields in conformal field theory. A Lie pseudoalgebra is a generalization of this structure, for which the algebra…
The invariant eigendistributions on a reductive Lie algebra are solutions of a holonomic D-module which has been proved to be regular by Kashiwara-Hotta. We solve here a conjecture of Sekiguchi saying that in the more general case of…
The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a…
In this article we investigate a pair of surjective local ring maps $S_1\leftarrow R\to S_2$ and their relation to the canonical projection $R\to S_1\otimes_R S_2$, where $S_1,S_2$ are Tor-independent over $R$. Our main result asserts a…
This paper is concerned with the subduction problem of type A quantum Iwahori-Hecke algebras $\mathbb{C} \mathbf{H}(\mathfrak{S}_f,q^2)$ with a real deformation parameter $q$, i.e. the problem of decomposing irreducible representations of…
The Stirling numbers of the second kind are related to normal orderings in the Weyl algebra, while the unsigned Stirling numbers of the first kind are related to normal orderings in the shift algebra. Kim-Kim introduced a {\lambda}-analogue…
In this paper we categorify the q-Schur algebra S(n,d) as a quotient of Khovanov and Lauda's diagrammatic 2-category U(sln). We also show that our 2-category contains Soergel's monoidal category of bimodules of type A, which categorifies…
This is a companion paper our previous submission "\infty-categories monoidales rigides et caracteres de Chern", in which we give a comparison between functions on the derived loop space of a smooth scheme of caracteristic zero, and its…