Dominant maximal weights of highest weight modules and Young tableaux

Jang Soo Kim, Kyu Hwan Lee, Se Jin Oh

Research output: Contribution to conferencePaperpeer-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 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.

Original languageEnglish
StatePublished - 2006
Event29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017 - London, United Kingdom
Duration: 9 Jul 201713 Jul 2017

Conference

Conference29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017
Country/TerritoryUnited Kingdom
CityLondon
Period9/07/1713/07/17

Bibliographical note

Funding Information:
∗The work was supported by NRF grants #2016R1D1A1A09917506 and #2016R1A5A1008055. †This work was partially supported by a grant from the Simons Foundation (#324706). ‡This work was supported by NRF Grant #2016R1C1B2013135.

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

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