Asymptotic dimension of invariant subspace in tensor product representation of compact Lie group

スポンサーリンク

概要

• 論文の詳細を見る

• We consider asymptotic behavior of the dimension of the invariant subspace in a tensor product of several irreducible representations of a compact Lie group G. It is equivalent to studying the symplectic volume of the symplectic quotient for a direct product of several coadjoint orbits of G. We obtain two formulas for the asymptotic dimension. The first formula takes the form of a finite sum over tuples of elements in the Weyl group of G. Each term is given as a multiple integral of a certain polynomial function. The second formula is expressed as an infinite series over dominant weights of G. This could be regarded as an analogue of Witten’s volume formula in 2-dimensional gauge theory. Each term includes data such as special values of the characters of the irreducible representations of G associated to the dominant weights.

• 社団法人 日本数学会の論文
• 2009-07-01

著者

• Suzuki Taro

  Graduate School Of Science And Engineering Chuo University

• TAKAKURA Tatsuru

  Department of Mathematics Chuo University

関連論文

• Asymptotic dimension of invariant subspace in tensor product representation of compact Lie group
• On vector partition functions with negative weights (Geometry of Transformation Groups and Combinatorics)

スポンサーリンク