Counting the maximal dominant weights of the irreducible \hat{sl}(n)-module of the highest weight kΛ_0
- 주제(키워드) 도움말 affine Kac-Moody algebra , maximal dominant weights
- 발행기관 서강대학교 일반대학원
- 지도교수 오영탁
- 발행년도 2016
- 학위수여년월 2016. 2
- 학위명 석사
- 학과 및 전공 일반대학원 수학과
- 실제URI http://www.dcollection.net/handler/sogang/000000058935
- 본문언어 영어
- 저작권 서강대학교 논문은 저작권보호를 받습니다.
초록/요약
Kac-Moody algebras were discovered by Kac and Moody independently in the middle of 1960's. In particular, affine Kac-Moody algebras are a family of infinite dimensional Kac-Moody algebras which has strong connections to other areas such as number theory, combinatorics, and mathematical physics. Recently, Jayne and Misra succeeded in finding all maximal dominant weights of special \hat{sl}(n)-modules. In addition, they proposed a conjecture on the number of maximal dominant weights of the \hat{sl}(n)-module V(kΛ_0), where n and k are arbitrary positive integers. The aim of this thesis is to study this conjecture. We first construct a bijection from the set of all maximal dominant weights of \hat{sl}(n)-module V(kΛ_0) to that of all maximal dominant weights of \hat{sl}(k)-module V(nΛ_0) for arbitrary positive integers n,k \geq 2. And then, we prove that this conjecture is affirmative when n and k are relatively prime by constructing a bijection between the set of all maximal dominant weights of \hat{sl}(n)-module V(kΛ_0) to that of all necklaces with n white beads and k black beads.
more