Intertwining numbers; the $n$-rowed shapes

Title:

Intertwining numbers; the $n$-rowed shapes

Creator:

Ko, Hyoung J. and Lee, Kyoung J.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:90cae2b8-a7b9-4bfd-a6b8-1a1dafce0d96
uuid:90cae2b8-a7b9-4bfd-a6b8-1a1dafce0d96

Subject:

representation theory, intertwining number, Weyl module, $\mathop {\mathrm Ext}\nolimits $ group, and partition

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

A fairly old problem in modular representation theory is to determine the vanishing behavior of the $\mathop {\mathrm Hom}\nolimits $ groups and higher $\mathop {\mathrm Ext}\nolimits $ groups of Weyl modules and to compute the dimension of the $\mathbb{Z} /(p)$-vector space $\mathop {\mathrm Hom}\nolimits _{\bar{A}_r}(\bar{K}_\lambda ,\bar{K}_\mu )$ for any partitions $\lambda $, $\mu $ of $r$, which is the intertwining number. K. Akin, D. A. Buchsbaum, and D. Flores solved this problem in the cases of partitions of length two and three. In this paper, we describe the vanishing behavior of the groups $\mathop {\mathrm Hom}\nolimits _{\bar{A}_r}(\bar{K}_\lambda ,\bar{K}_\mu )$ and provide a new formula for the intertwining number for any $n$-rowed partition.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

53-65

Source:

Czechoslovak Mathematical Journal | 2007 Volume:57 | Number:1

Harvested from:

CDK

Metadata only:

false