Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493520 | Journal of Algebra | 2005 | 26 Pages |
Abstract
We propose a conjecture describing the branching rule, in terms of Littelmann's path model, from the special linear Lie algebra sl2n(C) (of type A2nâ1) to the symplectic Lie algebra (of type Cn) embedded as the fixed point subalgebra of the diagram automorphism of sl2n(C). Moreover, we prove the conjecture in certain cases, and also provide some supporting examples. In addition, we show that the branching coefficients can be obtained explicitly by using the inverse Kostka matrix and path models for tensor products of symmetric powers of the defining (or natural) representation C2n of sl2n(C).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Satoshi Naito, Daisuke Sagaki,