UNITARY REPRESENTATIONS OF CYCLOTOMIC HECKE ALGEBRAS AT ROOTS OF UNITY: COMBINATORIAL CLASSIFICATION AND BGG RESOLUTIONS

被引：2

作者：

Bowman, Chris ^{[1
]}

Norton, Emily ^{[2
]}

Simental, Jose ^{[3
]}

机构：

[1] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England

[2] Univ Kent, Sch Math Stat & Actuarial Sci, Canterbury, Kent, England

[3] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico

来源：

JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU | 2024年 / 23卷 / 02期

基金：

欧洲研究理事会; 英国工程与自然科学研究理事会;

关键词：

HIGHEST WEIGHT CATEGORIES; SPLITTABLE REPRESENTATIONS;

D O I：

10.1017/S147474802200055X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We relate the classes of unitary and calibrated representations of cyclotomic Hecke algebras, and, in particular, we show that for the most important deformation parameters these two classes coincide. We classify these representations in terms of both multipartition combinatorics and as the points in the fundamental alcove under the action of an affine Weyl group. Finally, we cohomologically construct these modules via BGG resolutions.

引用

页码：557 / 608

页数：52

共 44 条

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C. Bowman
E. Norton
J. Simental
Selecta Mathematica, 2022, 28
[2] On BGG resolutions of unitary modules for quiver Hecke and Cherednik algebras
Bowman, C.
Norton, E.
Simental, J.
SELECTA MATHEMATICA-NEW SERIES, 2022, 28 (02):
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Griffeth, Stephen
JOURNAL OF ALGEBRA, 2018, 512 : 310 - 356

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