Dominant maximal weights of highest weight modules and Young tableaux

Jang Soo Kim; Kyu Hwan Lee; Se Jin Oh

Dominant maximal weights of highest weight modules and Young tableaux

Jang Soo Kim, Kyu Hwan Lee, Se Jin Oh

Department of Mathematics

Research output: Contribution to conference › Paper › peer-review

1 Scopus citations

Abstract

We study the multiplicities of dominant maximal weights of integrable highest weight modules V(λ) with highest weights λ, including all fundamental weights, over affine Kac-Moody algebras of types B_n⁽¹⁾, D_n⁽¹⁾, A_2n-¹⁽²⁾, A_2n⁽²⁾, D_n+1⁽¹⁾. We introduce new families of Young tableaux, called the almost even tableaux and (spin) rigid tableaux, and prove that they enumerate the crystal basis elements of dominant maximal weight spaces. By applying inductive insertion schemes for tableaux, in some special cases we prove that the weight multiplicities of maximal weights form the Pascal, Motzkin, Riordan and Bessel triangles.

Original language	English
State	Published - 2006
Event	29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017 - London, United Kingdom Duration: 9 Jul 2017 → 13 Jul 2017

Conference

Conference	29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017
Country/Territory	United Kingdom
City	London
Period	9/07/17 → 13/07/17

Bibliographical note

Publisher Copyright:
© 29th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.

Keywords

Crystal basis
Dominant maximal weight
Motzkin triangle
Pascal triangle
Riordan triangle
Young tableaux

Cite this

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title = "Dominant maximal weights of highest weight modules and Young tableaux",

abstract = "We study the multiplicities of dominant maximal weights of integrable highest weight modules V(λ) with highest weights λ, including all fundamental weights, over affine Kac-Moody algebras of types Bn(1), Dn(1), A2n-1(2), A2n(2), Dn+1(1). We introduce new families of Young tableaux, called the almost even tableaux and (spin) rigid tableaux, and prove that they enumerate the crystal basis elements of dominant maximal weight spaces. By applying inductive insertion schemes for tableaux, in some special cases we prove that the weight multiplicities of maximal weights form the Pascal, Motzkin, Riordan and Bessel triangles.",

keywords = "Crystal basis, Dominant maximal weight, Motzkin triangle, Pascal triangle, Riordan triangle, Young tableaux",

author = "Kim, {Jang Soo} and Lee, {Kyu Hwan} and Oh, {Se Jin}",

note = "Publisher Copyright: {\textcopyright} 29th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.; 29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017 ; Conference date: 09-07-2017 Through 13-07-2017",

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TY - CONF

T1 - Dominant maximal weights of highest weight modules and Young tableaux

AU - Kim, Jang Soo

AU - Lee, Kyu Hwan

AU - Oh, Se Jin

PY - 2006

Y1 - 2006

N2 - We study the multiplicities of dominant maximal weights of integrable highest weight modules V(λ) with highest weights λ, including all fundamental weights, over affine Kac-Moody algebras of types Bn(1), Dn(1), A2n-1(2), A2n(2), Dn+1(1). We introduce new families of Young tableaux, called the almost even tableaux and (spin) rigid tableaux, and prove that they enumerate the crystal basis elements of dominant maximal weight spaces. By applying inductive insertion schemes for tableaux, in some special cases we prove that the weight multiplicities of maximal weights form the Pascal, Motzkin, Riordan and Bessel triangles.

AB - We study the multiplicities of dominant maximal weights of integrable highest weight modules V(λ) with highest weights λ, including all fundamental weights, over affine Kac-Moody algebras of types Bn(1), Dn(1), A2n-1(2), A2n(2), Dn+1(1). We introduce new families of Young tableaux, called the almost even tableaux and (spin) rigid tableaux, and prove that they enumerate the crystal basis elements of dominant maximal weight spaces. By applying inductive insertion schemes for tableaux, in some special cases we prove that the weight multiplicities of maximal weights form the Pascal, Motzkin, Riordan and Bessel triangles.

KW - Crystal basis

KW - Dominant maximal weight

KW - Motzkin triangle

KW - Pascal triangle

KW - Riordan triangle

KW - Young tableaux

UR - http://www.scopus.com/inward/record.url?scp=85091956637&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:85091956637

T2 - 29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017

Y2 - 9 July 2017 through 13 July 2017

ER -

Dominant maximal weights of highest weight modules and Young tableaux

Abstract

Conference

Bibliographical note

Keywords

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