15 citations · 97 across the 32 of their papers we have counts for
20 papers · 1 filter
Pascal, Catalan, Motzkin triangles and tensor product multiplicities
L. Poulain d'Andecy
The main purpose of this note is to provide an elementary discussion of some simple triangles of integer numbers in particular through their connections with representation theory…
Kazhdan-Lusztig bases of parabolic Hecke algebras and applications to Schur-Weyl duality
Jeremie Guilhot, Loic Poulain d'Andecy
With an eye to applications to type A and Schur-Weyl duality, we study Kazhdan-Lusztig bases for a general parabolic Hecke algebra. Parabolic Hecke algebras are idempotent subalgeb…
The orientifold Temperley--Lieb algebra
Chris Bowman, Zajj Daugherty, Maud De Visscher +2
We construct gradings on the simple modules of 2-boundary Temperley--Lieb algebras and symplectic blob algebras by realising the latter algebras as quotients of Varagnolo--Vasserot…
Little -Jacobi polynomials and symmetry breaking operators for
Quentin Labriet, Loïc Poulain d'Andecy
This paper presents explicit formulas for intertwining operators of the quantum group acting on tensor products of Verma modules. We express a first set of intertwining…
Framization of Schur--Weyl duality and Yokonuma--Hecke type algebras
Abel Lacabanne, Loïc Poulain d'Andecy
We study framizations of algebras through the idea of Schur--Weyl duality. We provide a general setting in which framizations of algebras such as the Yokonuma--Hecke algebra natura…
Fused Hecke algebra and one-boundary algebras
L. Poulain d'Andecy, M. Zaimi
This paper gives an algebraic presentation of the fused Hecke algebra which describes the centraliser of tensor products of the -representation labelled by a one-row par…
Identities for Rankin-Cohen brackets, Racah coefficients and associativity
Quentin Labriet, Loic Poulain d'Andecy
We prove an infinite family of identities satisfied by the Rankin-Cohen brackets involving the Racah polynomials. A natural interpretation in the representation theory of sl(2) is…
Centralisers and Hecke algebras in Representation Theory, with applications to Knots and Physics
L. Poulain d'Andecy
This document is a thesis presented for the ``Habilitation à diriger des recherches''. The first chapter provides some background and sketch the story of the classical Schur-Weyl d…
Realisations of Racah algebras using Jacobi operators and convolution identities
Q. Labriet, L. Poulain d'Andecy
Using the representation theory of sl(2) and an appropriate model for tensor product of lowest weight Verma modules, we give a realisation first of the Hahn algebra, and then of th…
Askey-Wilson braid algebra and centralizer of
Nicolas Crampe, Loic Poulain d'Andecy, Luc Vinet +1
A presentation of the centralizer of the three-fold tensor product of the spin representation of the quantum group is provided. It is expressed as a quot…
Racah algebras, the centralizer and its Hilbert-Poincaré series
Nicolas Crampe, Julien Gaboriaud, Loïc Poulain d'Andecy +1
The higher rank Racah algebra introduced recently is recalled. A quotient of this algebra by central elements, which we call the special Racah algebra , is then intro…
Fused braids and centralisers of tensor representations of
N. Crampe, L. Poulain d'Andecy
We present in this paper the algebra of fused permutations and its deformation the fused Hecke algebra. The first one is defined on a set of combinatorial objects that we call fuse…
Temperley-Lieb, Brauer and Racah algebras and other centralizers of su(2)
Nicolas Crampe, Loïc Poulain d'Andecy, Luc Vinet
In the spirit of the Schur-Weyl duality, we study the connections between the Racah algebra and the centralizers of tensor products of three (possibly different) irreducible repres…
Affine Hecke algebras and generalisations of quiver Hecke algebras for type B
L. Poulain d'Andecy, R. Walker
We define and study cyclotomic quotients of affine Hecke algebras of type B. We establish an isomorphism between direct sums of blocks of these algebras and a generalisation, for t…
Clifford theory for Yokonuma--Hecke algebras and deformation of complex reflection groups
N. Jacon, L. Poulain d'Andecy
We define and study an action of the symmetric group on the Yokonuma--Hecke algebra. This leads to the definition of two classes of algebras. The first one is connected with the im…
Young tableaux and representations of Hecke algebras of type ADE
L. Poulain d'Andecy
We introduce and study some affine Hecke algebras of type ADE, generalising the affine Hecke algebras of GL. We construct irreducible calibrated representations and describe the ca…
An isomorphism Theorem for Yokonuma--Hecke algebras and applications to link invariants
N. Jacon, L. Poulain d'Andecy
We develop several applications of the fact that the Yokonuma--Hecke algebra of the general linear group GL is isomorphic to a direct sum of matrix algebras associated to Iwahori--…
Fusion procedure for wreath products of finite groups by the symmetric group
L. Poulain d'Andecy
Let G be a finite group. A complete system of pairwise orthogonal idempotents is constructed for the wreath product of G by the symmetric group by means of a fusion procedure, that…
Jucys--Murphy elements and representations of cyclotomic Hecke algebras
O. V. Ogievetsky, L. Poulain d'Andecy
An inductive approach to the representation theory of cyclotomic Hecke algebras, inspired by Okounkov and Vershik, is developed. We study the common spectrum of the Jucys-Murphy el…
On representations of complex reflection groups G(m,1,n)
O. V. Ogievetsky, L. Poulain d'Andecy
An inductive approach to the representation theory of the chain of the complex reflection groups G(m,1,n) is presented. We obtain the Jucys-Murphy elements of G(m,1,n) from the Juc…