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Identities for hypergeometric integrals of different dimensions | | V.Tarasov
; A.Varchenko
; | | Date: |
15 May 2003 | | Subject: | Quantum Algebra; Mathematical Physics; Representation Theory | math.QA math-ph math.MP math.RT | | Abstract: | 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. | | Source: | arXiv, math.QA/0305224 | | Services: | Forum | Review | PDF | Favorites | |
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