Zobrazeno 1 - 10
of 54
pro vyhledávání: '"d'Andecy, L. Poulain"'
Autor:
d'Andecy, L. Poulain, Zaimi, M.
Publikováno v:
Pacific J. Math. 328 (2024) 77-118
This paper gives an algebraic presentation of the fused Hecke algebra which describes the centraliser of tensor products of the $U_q(gl_N)$-representation labelled by a one-row partition of any size with vector representations. It is obtained through
Externí odkaz:
http://arxiv.org/abs/2306.10937
Autor:
d'Andecy, L. Poulain
This document is a thesis presented for the ``Habilitation \`a diriger des recherches''. The first chapter provides some background and sketch the story of the classical Schur-Weyl duality and its quantum analogue involving the Hecke algebra. Quantum
Externí odkaz:
http://arxiv.org/abs/2304.00850
Autor:
Labriet, Q., d'Andecy, L. Poulain
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 the Racah algebra, using Jacobi differential operators. While doing so w
Externí odkaz:
http://arxiv.org/abs/2304.00820
Publikováno v:
Algebraic Combinatorics, Volume 7 (2024) no. 2, pp. 361-382
Bivariate P-polynomial association scheme of type $(\alpha,\beta)$ are defined as a generalization of the P-polynomial association schemes. This generalization is shown to be equivalent to a set of conditions on the intersection parameters. A number
Externí odkaz:
http://arxiv.org/abs/2212.10824
Autor:
d'Andecy, L. Poulain
Publikováno v:
Winter Braids Lecture Notes, Vol. 7 (2020), Course no III, p. 1--49
These are the extended notes of a mini-course given at the school WinterBraids X. We discuss algebras simultaneously related to: the braid group, the Yang-Baxter equation and the representation theory of quantum groups. The main goal is to explain th
Externí odkaz:
http://arxiv.org/abs/2204.03483
Publikováno v:
J. Lie Theory 31 (2021), no. 4, 1085--1112
Building on classical invariant theory, it is observed that the polarised traces generate the centraliser $Z_L(sl(N))$ of the diagonal embedding of $U(sl(N))$ in $U(sl(N))^{\otimes L}$. The paper then focuses on $sl(3)$ and the case $L=2$. A Calabi--
Externí odkaz:
http://arxiv.org/abs/2005.13444
Autor:
Crampe, N., d'Andecy, L. Poulain
Publikováno v:
Lett. Math. Phys. 111 (2021), no. 4, Paper No. 92, 21 pp
We give an explicit Baxterisation formula for the fused Hecke algebra and its classical limit for the algebra of fused permutations. These algebras replace the Hecke algebra and the symmetric group in the Schur--Weyl duality theorems for the symmetri
Externí odkaz:
http://arxiv.org/abs/2004.05035
Autor:
Crampe, N., d'Andecy, L. Poulain
Publikováno v:
Algebr. Represent. Theor. 26 (2023) 901--955
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 fused permutations, and its deformation is defined on a set of topological
Externí odkaz:
http://arxiv.org/abs/2001.11372
Autor:
d'Andecy, L. Poulain, Walker, R.
Publikováno v:
J. Algebra 552 (2020), 1--37
We define and study cyclotomic quotients of affine Hecke algebras of type D. We establish an isomorphism between (direct sums of blocks of) these cyclotomic quotients and a generalisation of cyclotomic quiver Hecke algebras which are a family of Z-gr
Externí odkaz:
http://arxiv.org/abs/1901.09978
Autor:
d'Andecy, L. Poulain, Walker, R.
Publikováno v:
Proc. Edinb. Math. Soc. (2) 63 (2020), no. 2, 531--578
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 type B, of cyclotomic quiver Hecke algebras which are a family of grade
Externí odkaz:
http://arxiv.org/abs/1712.05592