Finite-dimensional representations of the elliptic modular double View Full Text


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Article Info

DATE

2015-05

AUTHORS

S. E. Derkachov, V. P. Spiridonov

ABSTRACT

We investigate the kernel space of an integral operator M(g) depending on the “spin” g and describing an elliptic Fourier transformation. The operator M(g) is an intertwiner for the elliptic modular double formed from a pair of Sklyanin algebras with the parameters η and τ, Imτ > 0, Imη > 0. For two-dimensional lattices g = nη + mτ/2 and g = 1/2 + nη + mτ/2 with incommensurate 1, 2η, τand integers n,m > 0, the operator M(g) has a finite-dimensional kernel that consists of the products of theta functions with two different modular parameters and is invariant under the action of generators of the elliptic modular double. More... »

PAGES

597-618

References to SciGraph publications

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  • 2001-12. Clebsch–Gordan and Racah–Wigner Coefficients for a Continuous Series of Representations of ?q (??(2, ℝ)) in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11232-015-0284-0

    DOI

    http://dx.doi.org/10.1007/s11232-015-0284-0

    DIMENSIONS

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