Zelevinsky's involution at roots of unity

Kashiwara and Zelevinsky involutions in affine type A

We first describe how the Kashiwara involution on crystals of affine type $A$ is encoded by the combinatorics of aperiodic multisegments. This yields a simple relation between this involution and the Zelevinsky involution on the set of simple modules for the affine Hecke algebras. We then give efficient procedures for computing these involutions. Remarkably, these procedures do not use the underlying crystal structure. They also permit to match explicitly the Ginzburg and Ariki parametrizations of the simple modules associated to affine and cyclotomic Hecke algebras, respectively .

Quantum Groups, Roots of Unity and Particles on quantized Anti-de Sitter Space

Quantum groups in general and the quantum Anti-de Sitter group $U_q(so(2,3))$ in particular are studied from the point of view of quantum field theory. We show that if $q$ is a suitable root of unity, there exist finite-dimensional, unitary representations corresponding to essentially all the classical one-particle representations with (half)integer spin, with the same structure at low energies as in the classical case. In the massless case for spin $\geq 1$, the "naive" representations are unitarizable only after factoring out a subspace of "pure gauges", as classically. Unitary many-particle…

量子对称对在单位根处的表示

Representations of quantum symmetric pairs at roots of unity

本文研究量子对称对在单位根处的表示结构，确定其不可约表示参数化及最大维度，并探讨其分支问题。