Intertwining numbers; the n -rowed shapes

Hyoung J. Ko; Kyoung J. Lee

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 1, page 53-65
  • ISSN: 0011-4642

Abstract

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A fairly old problem in modular representation theory is to determine the vanishing behavior of the H o m groups and higher E x t groups of Weyl modules and to compute the dimension of the ℤ / ( p ) -vector space H o m A ¯ r ( K ¯ λ , K ¯ μ ) for any partitions λ , μ 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 H o m A ¯ r ( K ¯ λ , K ¯ μ ) and provide a new formula for the intertwining number for any n -rowed partition.

How to cite

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Ko, Hyoung J., and Lee, Kyoung J.. "Intertwining numbers; the $n$-rowed shapes." Czechoslovak Mathematical Journal 57.1 (2007): 53-65. <http://eudml.org/doc/31112>.

@article{Ko2007,
abstract = {A fairly old problem in modular representation theory is to determine the vanishing behavior of the $\mathop \{\mathrm \{H\}om\}\nolimits $ groups and higher $\mathop \{\mathrm \{E\}xt\}\nolimits $ groups of Weyl modules and to compute the dimension of the $\mathbb \{Z\} /(p)$-vector space $\mathop \{\mathrm \{H\}om\}\nolimits _\{\bar\{A\}_r\}(\bar\{K\}_\lambda ,\bar\{K\}_\mu )$ 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 $\mathop \{\mathrm \{H\}om\}\nolimits _\{\bar\{A\}_r\}(\bar\{K\}_\lambda ,\bar\{K\}_\mu )$ and provide a new formula for the intertwining number for any $n$-rowed partition.},
author = {Ko, Hyoung J., Lee, Kyoung J.},
journal = {Czechoslovak Mathematical Journal},
keywords = {representation theory; intertwining number; Weyl module; $\mathop \{\mathrm \{E\}xt\}\nolimits $ group; partition; modular representations; intertwining numbers; Weyl modules},
language = {eng},
number = {1},
pages = {53-65},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Intertwining numbers; the $n$-rowed shapes},
url = {http://eudml.org/doc/31112},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Ko, Hyoung J.
AU - Lee, Kyoung J.
TI - Intertwining numbers; the $n$-rowed shapes
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 53
EP - 65
AB - A fairly old problem in modular representation theory is to determine the vanishing behavior of the $\mathop {\mathrm {H}om}\nolimits $ groups and higher $\mathop {\mathrm {E}xt}\nolimits $ groups of Weyl modules and to compute the dimension of the $\mathbb {Z} /(p)$-vector space $\mathop {\mathrm {H}om}\nolimits _{\bar{A}_r}(\bar{K}_\lambda ,\bar{K}_\mu )$ 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 $\mathop {\mathrm {H}om}\nolimits _{\bar{A}_r}(\bar{K}_\lambda ,\bar{K}_\mu )$ and provide a new formula for the intertwining number for any $n$-rowed partition.
LA - eng
KW - representation theory; intertwining number; Weyl module; $\mathop {\mathrm {E}xt}\nolimits $ group; partition; modular representations; intertwining numbers; Weyl modules
UR - http://eudml.org/doc/31112
ER -

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