Finiteness of a cohomology associated with certain Jackson integrals
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Publication:1177402
DOI10.2748/tmj/1178227537zbMath0769.33016OpenAlexW2099378552MaRDI QIDQ1177402
Publication date: 26 June 1992
Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2748/tmj/1178227537
Elliptic curves (14H52) Theta functions and abelian varieties (14K25) Basic hypergeometric integrals and functions defined by them (33D60) Almost homogeneous manifolds and spaces (32M12) General theory of automorphic functions of several complex variables (32N05)
Related Items (18)
Quantized Knizhnik-Zamolodchikov equations, quantum Yang-Baxter equation, and difference equations for \(q\)-hypergeometric functions ⋮ q-analogue of de Rham cohomology associated with Jackson integrals. I ⋮ q-analogue of de Rham cohomology associated with Jackson integrals. II ⋮ Gauss decomposition of connection matrices for symmetric \(A\)-type Jackson integrals ⋮ An integral representation of eigenfunctions for Macdonald's \(q\)-difference operators ⋮ A bilateral extension of the $q$-Selberg integral ⋮ The \(q\)-Dixon-Anderson integral and multi-dimensional \(_1\psi_1\) summations ⋮ Askey-Wilson polynomials by means of a \(q\)-Selberg type integral ⋮ The Gauss-Manin connection of the integral of the deformed difference product ⋮ Quantum affine algebras and holonomic difference equations ⋮ Jackson integrals of Jordan-Pochhammer type and quantum Knizhnik-Zamolodchikov equations ⋮ Le langage des espaces et des groupes quantiques. (The language of quantum spaces and quantum groups) ⋮ Structure of Jackson integrals of \(BC_n\) type ⋮ A determinant formula associated with the elliptic hypergeometric integrals of type BC n ⋮ Deformations of \(W\)-algebras associated to simple Lie algebras ⋮ Quantum algebra structure of certain Jackson integrals ⋮ Holonomic \(q\)-difference system associated with the basic hypergeometric series \(_{n+1}\varphi_ n\) ⋮ Holonomic \(q\)-difference system of the first order associated with a Jackson integral of Selberg type
Cites Work
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- Lectures on torus embeddings and applications. (Based on joint work with Katsuya Miyake.)
- Gauss-Manin connection of integral of difference products
- A q-analog of the Gauss summation theorem for hypergeometric series in U(n)
- Theory of prehomogeneous vector spaces (algebraic part)—the English translation of Sato’s lecture from Shintani’s note
- Some Basic Hypergeometric Extensions of Integrals of Selberg and Andrews
- Connection problem in holonomicq-difference system associated with a Jackson integral of Jordan-Pochhammer type
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