Related papers: Polynomialit\'e des coefficients de structure des …

These notes are an introduction to symplectic groupoids and the double structures associated with them. The treatment is intended to lie about midway between the original account of Coste, Dazord and Weinstein, which relied on effective use…

In this paper, we study the polynomial representation of the double affine Hecke algebra of type $(C^\vee_n, C_n)$ for specialized parameters. Inductively and combinatorially, we give a linear basis of the representation in terms of linear…

A conformal partition function ${\cal P}_n^m(s)$, which arose in the theory of Diophantine equations supplemented with additional restrictions, is concerned with {\it self-dual symmetric polynomials} -- reciprocal ${\sf R}^{\{m\}}_ {S_n}$…

In earlier joint work with A. Connes on transverse index theory on foliations, cyclic cohomology adapted to Hopf algebras has emerged as a decisive tool in deciphering the total index class of the hypoelliptic signature operator. We have…

The Hecke algebras $\mathcal{H}_{n,k}$ of the group pairs $(S_{kn}, S_k\wr S_n)$ can be endowed with a filtration with respect to the orbit structures of the elements of $S_{kn}$ relative to the action of $S_{kn}$ on the set of…

This paper investigates the independence polynomials arising from iterated strong products of cycle graphs, examining their algebraic symmetries and combinatorial structures. Leveraging modular arithmetic and Galois theory, we establish…

We describe dualities and complexes of logarithmic forms and differentials for central affine and corresponding projective arrangements. We generalize the Borel-Serre formula from vector bundles to sheaves on projective d-space with locally…

In [14] we introduced a new class of algebras, which we named \textit{quantum generalized Heisenberg algebras} and which depend on a parameter $q$ and two polynomials $f,g$. We have shown that this class includes all generalized Heisenberg…

The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…

We show how a novel construction of the sheaf of Cherednik algebras on a quotient orbifold Y=X/G by virtue of formal geometry in author's prior work leads to results for the sheaf of Cherednik algebra which until recently were viewed as…

Generalizations of the Hermite polynomials to many variables and/or to the complex domain have been located in mathematical and physical literature for some decades. Polynomials traditionally called complex Hermite ones are mostly…

Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras $\bigoplus_{n\ge0}A_n$ can be endowed with the structure of graded dual Hopf algebras. Hivert and Nzeutzhap, and…

We propose a new approach to study the Kronecker coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. We explain the limiting behavior and associated bounds in the context of the partition…

We introduce a central extension of the preprojective algebra of a finite Dynkin quiver (depending on a regular weight for the corresponding root system), whose natural deformed version is flat (unlike that for the preprojective algebra).…

The article is a contribution to the local theory of geometric Langlands correspondence. The main result is a categorification of the isomorphism between the (extended) affine Hecke algebra, thought of as an algebra of Iwahori bi-invariant…

We prove that the structure algebra of a Bruhat moment graph of a finite real root system is a Hopf algebroid with respect to the Hecke and the Weyl actions. We introduce new techniques (reconstruction and push-forward formula of a product,…

We first describe, over a field K of characteristic different from 2, the orbits for the adjoint actions of the Lie groups PGL(2, K) and PSL(2, K) on their Lie algebra sl(2, K). While the former are well known, the latter lead to the…

Polynomial functors are useful in the theory of data types, where they are often called containers. They are also useful in algebra, combinatorics, topology, and higher category theory, and in this broader perspective the polynomial aspect…

In this note we generalize the definition of partial permutations of Ivanov and Kerov and we build a universal algebra which projects onto the m-centraliser algebra defined by Creedon. We use it to present a new proof for the polynomiality…

We show that the characteristic polynomial of a hyperplane arrangement can be recovered from the class in the Grothendieck group of varieties of the complement of the arrangement. This gives a quick proof of a theorem of Orlik and Solomon…