Formal Affine Demazure and Hecke Algebras of Kac-Moody Root Systems

Baptiste Calmès; Kirill Zainoulline; Changlong Zhong

doi:10.1007/s10468-019-09880-w

Formal Affine Demazure and Hecke Algebras of Kac-Moody Root Systems

Baptiste Calmès
, Kirill Zainoulline
, Changlong Zhong

Mathematics and Statistics

University at Albany

Université d'Artois
University of Ottawa

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We define the formal affine Demazure algebra and a formal affine Hecke algebra associated to a Kac-Moody root system. We prove structure theorems for these algebras, and use them to extend several results and constructions (presentation in terms of generators and relations, coproduct and product structures, filtration by codimension of Bott-Samelson classes, root polynomials and multiplication formulas) that were previously known for finite root systems.

Original language	English
Pages (from-to)	1031-1050
Number of pages	20
Journal	Algebras and Representation Theory
Volume	23
Issue number	3
DOIs	https://doi.org/10.1007/s10468-019-09880-w
State	Published - Jun 1 2020

Keywords

Divided difference operator
Formal affine Demazure algebra
Kac-Moody root system
Oriented cohomology

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abstract = "We define the formal affine Demazure algebra and a formal affine Hecke algebra associated to a Kac-Moody root system. We prove structure theorems for these algebras, and use them to extend several results and constructions (presentation in terms of generators and relations, coproduct and product structures, filtration by codimension of Bott-Samelson classes, root polynomials and multiplication formulas) that were previously known for finite root systems.",

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AU - Zainoulline, Kirill

AU - Zhong, Changlong

PY - 2020/6/1

Y1 - 2020/6/1

N2 - We define the formal affine Demazure algebra and a formal affine Hecke algebra associated to a Kac-Moody root system. We prove structure theorems for these algebras, and use them to extend several results and constructions (presentation in terms of generators and relations, coproduct and product structures, filtration by codimension of Bott-Samelson classes, root polynomials and multiplication formulas) that were previously known for finite root systems.

AB - We define the formal affine Demazure algebra and a formal affine Hecke algebra associated to a Kac-Moody root system. We prove structure theorems for these algebras, and use them to extend several results and constructions (presentation in terms of generators and relations, coproduct and product structures, filtration by codimension of Bott-Samelson classes, root polynomials and multiplication formulas) that were previously known for finite root systems.

KW - Divided difference operator

KW - Formal affine Demazure algebra

KW - Kac-Moody root system

KW - Oriented cohomology

UR - https://www.scopus.com/pages/publications/85064158715

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DO - 10.1007/s10468-019-09880-w

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JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

IS - 3

ER -

Formal Affine Demazure and Hecke Algebras of Kac-Moody Root Systems

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Keywords

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