Identities between q-hypergeometric and hypergeometric integrals of different dimensions
Tarasov, V. ; Varchenko, A.
arXiv, 0309372 / Harvested from arXiv
Text on arXiv
Given complex numbers $m_1,l_1$ and nonnegative integers $m_2,l_2$, such that $m_1+m_2=l_1+l_2$, for any $a,b=0, ... ,\min(m_2,l_2)$ we define an $l_2$-dimensional Barnes type q-hypergeometric integral $I_{a,b}(z,\mu;m_1,m_2,l_1,l_2)$ and an $l_2$-dimensional hypergeometric integral $J_{a,b}(z,\mu;m_1,m_2,l_1,l_2)$. The integrals depend on complex parameters $z$ and $\mu$. We show that $I_{a,b}(z,\mu;m_1,m_2,l_1,l_2)$ equals $J_{a,b}(e^\mu,z;l_1,l_2,m_1,m_2)$ up to an explicit factor, thus establishing an equality of $l_2$-dimensional q-hypergeometric and $m_2$-dimensional hypergeometric integrals. The identity is based on the $(gl_k,gl_n)$ duality for the qKZ and dynamical difference equations.
Publié le : 2003-09-22
Classification:  Mathematics - Quantum Algebra,  Mathematical Physics,  Mathematics - Representation Theory 
@article{0309372,
     author = {Tarasov, V. and Varchenko, A.},
     title = {Identities between q-hypergeometric and hypergeometric integrals of
  different dimensions},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0309372}
}

Tarasov, V.; Varchenko, A. Identities between q-hypergeometric and hypergeometric integrals of
  different dimensions. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0309372/