Peter-Weyl Iwahori Algebras

Barbasch Dan; Moy Allen

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Peter-Weyl Iwahori Algebras

机译：Pethet R-Wyl Iwabori L Czie B等人。

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The Peter-Weyl idempotent e(p) of a parahoric subgroup P is the sum of the idempotents of irreducible representations of P that have a nonzero Iwahori fixed vector. The convolution algebra associated with e(p) is called a Peter-Weyl Iwahori algebra. We show that any Peter-Weyl Iwahori algebra is Morita equivalent to the Iwahori-Hecke algebra. Both the Iwahori-Hecke algebra and a Peter-Weyl Iwahori algebra have a natural conjugate linear anti-involution *, and the Morita equivalence preserves irreducible hermitian and unitary modules. Both algebras have another anti-involution, denoted by 4., and the Morita equivalence preserves irreducible and unitary modules for *.

机译：八卦子组P的Peter-Weyl Idempotent E（P）是具有非零IWAHORI固定载体的P的IDEMPOTENT的幂等。与e（p）相关的卷积代数称为彼得-Weyl iwahori代数。我们表明，任何Peter-Weyl Iwahori代数是莫里塔相当于Iwahori-Hecke代数。 iwahori-hecke代数和彼得 - Weyl iwahori代数都有一个天然的共轭线性抗联盟*，莫蒂塔等量保留了不可缩短的封闭件和酉模块。两种代数都有另一种抗联盟，由4表示，森田等量保留了*的不可缩短和单一模块。

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来源
《Canadian Journal of Mathematics》 |2020年第5期|共20页
作者
Barbasch Dan; Moy Allen;
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作者单位

Cornell Univ Dept Math Malott Hall Ithaca NY 14853 USA;

Hong Kong Univ Sci &

Technol Dept Math Clear Water Bay Rd Hong Kong Peoples R China;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
convolution algebra; Iwahori-Hecke algebra; idempotent; Morita equivalence; parahoric subgroup; Peter-Weyl idempotent; *-algebra;

机译：卷积代数;iwahori-hecke代数;Idempotent;莫里塔等价;普及亚组;彼得 - Weyl Idempotent;* - 代数;

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专利

1. Peter-Weyl Iwahori Algebras [J] . Barbasch Dan, Moy Allen Canadian Journal of Mathematics . 2020,第5期

机译：Pethet R-Wyl Iwabori L Czie B等人。
2. THE PRO-p-IWAHORI HECKE ALGEBRA OF A REDUCTIVE p-ADIC GROUP III (SPHERICAL HECKE ALGEBRAS AND SUPERSINGULAR MODULES) [J] . Vigneras Marie-France Journal of the Institute of Mathematics of Jussieu: JIMJ . 2017,第3期

机译：还原P-ADIC组III（球形HECKE代数和超周定模块）的Pro-p-iwahori Hecke代数
3. Classical link invariants from the framizations of the Iwahori-Hecke algebra and the Temperley-Lieb algebra of type A [J] . Goundaroulis D., Lambropoulou S. Journal of knot theory and its ramifications . 2017,第9期

机译：古典链接不变于iwahori-hecke代数的帧中化和type的Iwhery-lieb代数
4. Multiplicative Bases for the Centres of the Group Algebra and Iwahori-Hecke Algebra of the Symmetric Group [C] . Andrew Francis, Lenny Jones Southeastern Lie Theory Workshop on Combinatorial Lie Theory and Applications . 2012

机译：对称组的群代数和Iwahori-Hecke代数的乘法基础
5. Signed Permutation Modules of the Iwahori-Hecke Algebra [D] . Luo, Jietong. 2018

机译：IWAHORI-HECKE代数的签名置换模块
6. Quantum cluster algebras and quantum nilpotent algebras [O] . Kenneth R. Goodearl, Milen T. Yakimov 2014

机译：量子簇代数和量子幂等代数
7. A Ribbon Hopf Algebra Approach to the Irreducible Representations of Centralizer Algebras: The Brauer, Birman–Wenzl, and Type A Iwahori–Hecke Algebras [O] . Leduc Robert, Ram Arun 1997

机译：集中器代数的不可约表示的带状Hopf代数方法：Brauer，Birman-Wenzl和A型Iwahori-Hecke代数

Peter-Weyl Iwahori Algebras

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