Identities between q-hypergeometric and hypergeometric integrals of different dimensions
| dc.creator | Tarasov, V. | |
| dc.creator | Varchenko, A. | |
| dc.date | 2003-09-23 | |
| dc.date | 2004-04-04 | |
| dc.date.accessioned | 2026-07-07T05:01:22Z | |
| dc.date.available | 2026-07-07T05:01:22Z | |
| dc.description | 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 $I_{a,b}(z,μ;m_1,m_2,l_1,l_2)$ and an $l_2$-dimensional hypergeometric integral $J_{a,b}(z,μ;m_1,m_2,l_1,l_2)$. The integrals depend on complex parameters $z$ and $μ$. We show that $I_{a,b}(z,μ;m_1,m_2,l_1,l_2)$ equals $J_{a,b}(e^μ,z;l_1,l_2,m_1,m_2)$ 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. | |
| dc.description | Preprint (2003), 14 pages, AmsLaTeX, references updated | |
| dc.identifier | https://arxiv.org/abs/math/0309372 | |
| dc.identifier | http://arxiv.org/abs/math/0309372 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68643 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Mathematical Physics | |
| dc.subject | Representation Theory | |
| dc.title | Identities between q-hypergeometric and hypergeometric integrals of different dimensions | |
| dc.type | text |