Mehta Soya: A Promotional Conundrum

Difference Macdonald - Mehta conjecture

with respect to the Gaussian measure. Macdonald extended it from An−1 to other root systems and verified his conjecture for classical ones by means of the Selberg integrals [M1]. It was established by Opdam in [O1] in full generality using the shift operators. The integral is an important normalization constant for a k-deformation of the Hankel transform introduced by Dunkl [D]. The generalized...

On Cherednik–macdonald–mehta Identities

In this note we give a proof of Cherednik’s generalization of Macdonald–Mehta identities for the root system An−1, using representation theory of quantum groups. These identities give an explicit formula for the integral of a product of Macdonald polynomials with respect to a “difference analogue of the Gaussian measure”. They were suggested by Cherednik, who also gave a proof based on represen...

Diierence Macdonald-mehta Conjecture

Discrete analogues of Macdonald-Mehta integrals

Article history: Available online 15 July 2016

A developmental conundrum

Wnt signaling orchestrates morphogenetic processes in which changes in gene expression are associated with dramatic changes in cell organization within developing tissue/organs. Upon signaling, excess beta-catenin not utilized at cell-cell junctions becomes stabilized, where it can provide the transcriptional activating domain for Lef/Tcf DNA binding proteins. In skin epithelium, forced stabili...