On Base Partitions And Cover Partitions Of Skew Characters
Combinatorics
2008-08-11 v2 Representation Theory
Abstract
In this paper we give an easy combinatorial description for the base partition B of a skew character [A], which is the intersection of all partitions alpha whose corresponding character [alpha] appears in [A]. This we use to construct the cover partition C for the ordinary outer product as well as for the Schubert product of two characters and for some skew characters, here the cover partition is the union of all partitions whose corresponding character appears in the product or in the skew character. This gives us also the Durfee size for arbitrary Schubert products.
Keywords
Cite
@article{arxiv.0804.4626,
title = {On Base Partitions And Cover Partitions Of Skew Characters},
author = {Christian Gutschwager},
journal= {arXiv preprint arXiv:0804.4626},
year = {2008}
}
Comments
8 pages, v2: Remark 3.5 improved which made Section 5 in v1 redundant, some minor rewritings. to appear in Electron. J. Combin