### A family of tridiagonal pairs related to the quantum affine algebra ${U}_{q}\left(\widehat{{\text{sl}}_{2}}\right)$.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

The group SU(1,d) acts naturally on the Hilbert space $L\xb2\left(Bd{\mu}_{\alpha}\right)(\alpha >-1)$, where B is the unit ball of ${\u2102}^{d}$ and $d{\mu}_{\alpha}$ the weighted measure ${(1-|z\left|\xb2\right)}^{\alpha}dm\left(z\right)$. It is proved that the irreducible decomposition of the space has finitely many discrete parts and a continuous part. Each discrete part corresponds to a zero of the generalized Harish-Chandra c-function in the lower half plane. The discrete parts are studied via invariant Cauchy-Riemann operators. The representations on the discrete parts are equivalent to actions on some holomorphic...

We derive two identities for multiple basic hyper-geometric series associated with the unitary $U(n+1)$ group. In order to get the two identities, we first present two known $q$-exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two $U(n+1)$$q$-Chu-Vandermonde summations established by Milne, we arrive at our...

On donne une condition nécessaire et suffisante pour l’existence de modules de dimension finie sur l’algèbre de Cherednik rationnelle associée à un système de racines.