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A. Kazarnovski-Krol

Publications and source records attributed to A. Kazarnovski-Krol.

7 recordsLinked to original sources
arXiv1997

Matrix elements of vertex operators of deformed W-algebra and Harish Chandra Solutions to Macdonald's difference equations

In this paper we prove that certain matrix elements of vertex operators of deformed W-algebra satisfy Macdonald difference equations and form n! -dimensional space of solutions. These solutions are the analogues of Harish Chandra solutions with prescribed asymptotic behavior. We obtain formulas for analytic continuation as a consequence of braiding properties of vertex operators of deformed W-algebra.

q-alg↗
arXiv1997

Cycle for integration for zonal spherical function of type $A_n$

Integral of a certain multivalued form over cycle $\pmbΔ$ provides zonal spherical function of type $A_n$. This paper is devoted to quantum group analysis and verification of monodromy properties of the distinguished cycle $\pmbΔ$. Zonal spherical function is a particular conformal block of $WA_n$-algebra.

q-alg↗
arXiv1996

Variation on a theme of Selberg integral

In this paper we calculate some Generalized Selberg integrals. The answer is expressed in terms of $Γ$-functions. Integrals of this type serve as normalization constants or directly via undoing 2-D integrals for determination of structural constants of operator algebra.

q-alg↗
arXiv1995

Cycles for asymptotic solutions and Weyl group

In this paper cycles for asymptotic solutions for Heckman-Opdam hypergeometric system of type $A_n$ are described. Cycles are enumerated by elements of symmetric group. Leading asymptotic and leading coefficient are calculated. Value of certain multiple integral over special cycles is calculated with the help of result of Opdam.

q-alg↗
arXiv1995

Value of generalized hypergeometric function at unity

Value of generalized hypergeometric function at a special point is calculated. More precisely, value of certain multiple integral over vanishing cycle (all arguments collapse to unity) is calculated. The answer is expressed in terms of $Γ$-functions. The constant is relevant to the part of $ρ$ in the Gindikin-Karpelevich formula for c-function of Harish-Chandra. Calculation is an adaptation of classical calculations of Gelfand and Naimark (1950) to the Heckman-Opdam hypergeometric functions in the case of root system of type $A_{n-1}$.

hep-th↗