Kazufumi Kimoto

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math.RT2007

Representation theory of the $α$ -determinant and zonal spherical functions

Kazufumi Kimoto

We prove that the multiplicity of each irreducible component in the $U (gl_{n})$ -cyclic module generated by the $l$ -th power $det^{(α)} (X)^{l}$ of the $α$ -determin…

math.RT2007

Alpha-determinant cyclic modules and Jacobi polynomials

Kazufumi Kimoto, Sho Matsumoto, Masato Wakayama

We study the cyclic $U (gl_{n})$ -module generated by the $l$ -th power of the $α$ -determinant. When $l$ is a non-negative integer, for all but finite exceptional values of $…

Representation theory of the α-determinant and zonal spherical functions

Alpha-determinant cyclic modules and Jacobi polynomials

Representation theory of the $α$ -determinant and zonal spherical functions