Abstract:
For a space X acted on by a finite group Γ, the product space X n affords a natural action of the wreath product Γ n =Γn⋊S n . The direct sum of equivariant K-groups were shown earlier by the author to carry several interesting algebraic structures. In this paper we study the K-groups of Γ n -equivariant Clifford supermodules on X n. We show that is a Hopf algebra and it is isomorphic to the Fock space of a twisted Heisenberg algebra. Twisted vertex operators make a natural appearance. The algebraic structures on ℱ− Γ(X), when Γ is trivial and X is a point, specialize to those on a ring of symmetric functions with the Schur Q-functions as a linear basis. As a by-product, we present a novel construction of K-theory operations using the spin representations of the hyperoctahedral groups.
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Received: 3 February 2001 / Accepted: 17 August 2002 Published online: 10 January 2003
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Wang, W. Equivariant K-Theory, Generalized Symmetric Products, and Twisted Heisenberg Algebra. Commun. Math. Phys. 234, 101–127 (2003). https://doi.org/10.1007/s00220-002-0753-9
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DOI: https://doi.org/10.1007/s00220-002-0753-9