Identities for hypergeometric integrals of different dimensions
Tarasov, V. ; Varchenko, A.
arXiv, 0305224 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2003-05-15
Classification:  Mathematics - Quantum Algebra,  Mathematical Physics,  Mathematics - Representation Theory 
@article{0305224,
     author = {Tarasov, V. and Varchenko, A.},
     title = {Identities for hypergeometric integrals of different dimensions},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0305224}
}

Tarasov, V.; Varchenko, A. Identities for hypergeometric integrals of different dimensions. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0305224/