On the principal symbols of K_C-invariant differential operators on Hermitian symmetric spaces

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概要

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• Let (G,K) be one of the following Hermitian symmetric pair: (SU(p,q), S(U(p) × U(q))), (Sp(n,R), U(n)), or (SO*(2n), U(n)). Let GC and KC be the complexifications of G and K, respectively, Q the maximal parabolic subgroup of GC whose Levi part is KC, and V the holomorphic tangent space at the origin of G/K. It is known that the ring of KC-invariant differential operators on V has a generating system {Γk} given in terms of determinant or Pfaffian that plays an essential role in the Capelli identities. Our main result is that determinant or Pfaffian of a deformation of the twisted moment map on the holomorphic cotangent bundle of GC/Q provides a generating function for the principal symbols of Γks.

• 2011-07-01

著者

• Hashimoto Takashi

  Education Center Tottori University

関連論文

• On the principal symbols of K_C-invariant differential operators on Hermitian symmetric spaces

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