Branching Functions ofA(1)n−1and Jantzen–Seitz Problem for Ariki–Koike Algebras
✍ Scribed by Omar Foda; Bernard Leclerc; Masato Okado; Jean-Yves Thibon; Trevor A. Welsh
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 503 KB
- Volume
- 141
- Category
- Article
- ISSN
- 0001-8708
No coin nor oath required. For personal study only.
✦ Synopsis
We study the restrictions of simple modules of Ariki Koike algebras H m (v) with set of parameters v=(; v0 , ..., vl&1 ), where is an nth root of unity, to their subalgebras H m& j (v). Using a theorem of Ariki and the crystal basis theory of Kashiwara, we relate this problem to the calculation of tensor product multiplicities of highest weight irreductible representations of the affine Lie algebra A (1) n&1 . These multiplicities have a combinatorial description in terms of higher level paths or highest-lift multipartitions.
This enables us to solve the Jantzen Seitz problem for Ariki Koike algebras, that is, to determine which irreducible representations of H m (v) restrict to irreducible representations of H m&1 (v). From a combinatorial point of view, this problem is identical to that of computing the tensor product of an A (1) n&1 -module of level l and one of level 1.