Fusion Procedure for Cyclotomic BMW Algebras

被引：0
作者：
Weideng Cui
机构：
[1] Shandong University,School of Mathematics
来源：
Algebras and Representation Theory | 2018年 / 21卷
关键词：
Cyclotomic BMW algebra; Cyclotomic Nazarov-Wenzl algebra; Fusion procedure; Idempotents; 20C99; 05E10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we prove that the pairwise orthogonal primitive idempotents of generic cyclotomic Birman-Murakami-Wenzl algebras can be constructed by consecutive evaluations of a certain rational function. In the Appendix, we prove a similar result for generic cyclotomic Nazarov-Wenzl algebras. A consequence of the constructions is a one-parameter family of fusion procedures for the cyclotomic Hecke algebra and its degenerate analogue.
引用
收藏
页码：565 / 578
页数：13
相关论文
共 60 条
[1]  
Ariki S(1994)A Hecke algebra of $(\mathbb {Z}/r\mathbb {Z})\mathfrak {S}_{n}$(ℤ/rℤ)Sn and construction of its irreducible representations Adv. Math. 106 216-243
[2]  
Koike K(2006)Cyclotomic Nazarov-Wenzl algebras Nagoya Math. J. 182 47-134
[3]  
Ariki S(1989)Braids, link polynomials and a new algebra Trans. Amer. Math. Soc. 313 249-273
[4]  
Mathas A(1986)Special bases of irreducible representations of a degenerate affine Hecke algebra Funct. Anal. Appl. 20 76-78
[5]  
Rui H(1998)Cyclotomic q-Schur algebras Math. Z. 229 385-416
[6]  
Birman JS(2009)Cellularity of cyclotomic Birman-Wenzl-Murakami algebras J. Algebra. 321 3299-3320
[7]  
Wenzl H(2010)Comparison of admissible conditions for cyclotomic Birman-Wenzl-Murakami algebras J. Pure Appl. Algebra 214 2009-2016
[8]  
Cherednik I(2011)Admissibility conditions for degenerate cyclotomic BMW algebras Comm. Algebra 39 452-461
[9]  
Dipper R(2012)Remarks on cyclotomic and degenerate cyclotomic BMW algebras J. Algebra. 364 13-37
[10]  
James G(2009)Cyclotomic Birman-Wenzl-Murakami algebras, I. Freeness and realization as tangle algebras J. Knot Theory Ramifications 18 1089-1127
123456