過去の記録 ~12/10次回の予定今後の予定 12/11~

開催情報 火曜日 16:30~18:00 数理科学研究科棟(駒場) 126号室
担当者 小林俊行


14:30-16:00   数理科学研究科棟(駒場) 122号室
Soo Teck Lee 氏 (Singapore National University)
Pieri rule and Pieri algebras for the orthogonal groups (ENGLISH)
[ 講演概要 ]

The irreducible rational representations of the complex orthogonal
group $\\mathrm{O}_n$ are labeled by a certain set of Young diagrams,
and we denote the representation corresponding to the Young diagram
$D$ by $\\sigma^D_n$. Consider the tensor product
$\\sigma^D_n\\otimes\\sigma^E_n$ of two such representations. It can
be decomposed as
where for each Young diagram $F$ in the sum, $m_F$ is the
multiplicity of $\\sigma^F_n$ in $\\sigma^D_n\\otimes\\sigma^E_n$. In
the case when the Young diagram $E$ consists of only one row, a
description of the multiplicities in $\\sigma^D_n\\otimes\\sigma^E_n$
is called the {\\em Pieri Rule}. In this talk, I shall describe a
family of algebras whose structure encodes a generalization of the
Pieri Rule.