学术动态

25-05-2023

Skew Howe duality and limit shapes for Young diagrams

Title: Skew Howe duality and limit shapes for Young diagrams

(joint work with A.Nazarov and T.Schrimshaw)

Speaker: Olga Postnova (Saint Petersburg department of Steklov Mathematical Institute)

Time: 15:00-16:00 26/05/2023

Venue: LiDe Building 407

Abstract: Consider the exterior algebra of the tensor product of two complex vector spaces of dimension n and k. This space could be regarded as a bimodule for the action of dual pairs of Lie groups. For example, for GL(n) x GL(k) - case this exterior algebra decomposes into direct sum of bimodules parametrised by conjugate partitions inside the n x k rectangle. This is the skew Howe duality. On the level of characters the skew Howe duality yields the dual Cauchy identity for the Schur functions.

We interpret the skew Howe duality as a natural consequence of lattice paths on lozenge tilings of certain partial hexagonal domains. This combinatorial approach also allows to obtain product formulas for the q-deformations of multiplicities or different dual pairs of Lie groups . We consider the corresponding probability measures on Young diagrams and prove the uniform convergence to the limit shape of Young diagrams in the limit when n and k go to infinity.


学院办公室:010-82507161

本科生教务:010-62513386

研究生教务与国际交流:010-82507161

党团学办公室:010-62515886

在职课程培训班:010-82507075

 

邮编:100872

电话:010-82507161

传真:010-62513316

E-mail:mathruc@ruc.edu.cn/mathrucdw@ruc.edu.cn

地址:北京市海淀区中关村大街59号金沙集团1862cc橙色数学楼

金沙集团1862cc橙色公众号

版权所有 金沙集团1862cc橙色(中国)有限公司-搜狗百科 升星提供技术服务