Identities for hypergeometric integrals of different dimensions

V. Tarasov; A. Varchenko

Identities for hypergeometric integrals of different dimensions

量子代数 2007-05-23 v3 数学物理 math.MP 表示论

作者: V. Tarasov , A. Varchenko

摘要

Given complex numbers $m_1,l_1$ and positive integers $m_2,l_2$ , such that $m_1+m_2=l_1+l_2$ , we define $l_2$ -dimensional hypergeometric integrals $I_{a,b}(z;m_1,m_2,l_1,l_2)$ , $a,b=0,...,\min(m_2,l_2)$ , depending on a complex parameter $z$ . We show that $I_{a,b}(z;m_1,m_2,l_1,l_2)=I_{a,b}(z;l_1,l_2,m_1,m_2)$ , thus establishing an equality of $l_2$ and $m_2$ -dimensional integrals. This identity allows us to study asymptotics of the integrals with respect to their dimension in some examples. The identity is based on the $(gl_k,gl_n)$ duality for the KZ and dynamical differential equations.

关键词

hypergeometric functions

引用

@article{arxiv.math/0305224,
  title  = {Identities for hypergeometric integrals of different dimensions},
  author = {V. Tarasov and A. Varchenko},
  journal= {arXiv preprint arXiv:math/0305224},
  year   = {2007}
}

备注

Preprint (2003), 9 pages, AmsLaTeX, misprints corrected

Identities for hypergeometric integrals of different dimensions

摘要

关键词

引用

备注

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