CELLULAR STRUCTURES USING Uq-TILTING MODULES

被引：36
作者：
Andersen, Henning Haahr [1 ]
Stroppel, Catharina [2 ]
Tubbenhauer, Daniel [2 ]
机构：
[1] Aarhus Univ, Nat Videnskabelige Fak, QGM, Aarhus, Denmark
[2] Univ Bonn, Math Inst, Bonn, Germany
来源：
PACIFIC JOURNAL OF MATHEMATICS | 2018年 / 292卷 / 01期
关键词：
cellular algebras; cellular bases; tilting modules; quantum enveloping algebras; HIGHEST WEIGHT CATEGORIES; SCHUR-WEYL DUALITY; WALLED BRAUER ALGEBRAS; TENSOR-PRODUCTS; QUANTUM GROUPS; CRYSTAL BASES; ROOTS; REPRESENTATIONS; DECOMPOSITION; RECIPROCITY;
D O I：
10.2140/pjm.2018.292.21
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We use the theory of U-q-tilting modules to construct cellular bases for centralizer algebras. Our methods are quite general and work for any quantum group U-q attached to a Cartan matrix and include the nonsemisimple cases for q being a root of unity and ground fields of positive characteristic. Our approach also generalizes to certain categories containing infinite-dimensional modules. As applications, we give a new semisimplicity criterion for centralizer algebras, and we recover the cellularity of several known algebras (with partially new cellular bases) which all fit into our general setup.
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页码：21 / 59
页数：39
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