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2 results

  • Symmetry Classification for Jackson Integrals Associated with the Root System BCn

  • Masahiko Ito
  • Journal:
    Compositio Mathematica / Volume 136 / Issue 2 / April 2003
    Published online by Cambridge University Press:
    04 December 2007, pp. 209-216
    Print publication:
    April 2003
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  • The Jackson integrals associated with the non-reduced root system are defined as multiple sums which are generalization of the Bailey's very-well-poised 6ψ6 sum. They are classified by the number of their parameters when they can be expressed as a product of the Jacobi elliptic theta functions. The sums which appear in the classification list coincide with those investigated individually by Gustafson and van Diejen.

  • Symmetry Classification for Jackson Integrals Associated with Irreducible Reduced Root Systems

  • Masahiko Ito
  • Journal:
    Compositio Mathematica / Volume 129 / Issue 3 / December 2001
    Published online by Cambridge University Press:
    04 December 2007, pp. 325-340
    Print publication:
    December 2001
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  • We state certain product formulae for Jackson integrals associated with irreducible reduced root systems. The Jackson integral is defined here as a sum over any full-rank sublattice of the coweight lattice for the root system. In particular, a Weyl group symmetry classification of the Jackson integrals is done when they have an expression of a product of the Jacobi elliptic theta functions. Most of the product formulae investigated by Aomoto, Macdonald and Gustafson appear in the list of classifications. A new product formula for an F4 root system is included in it.