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Abstract
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Physicists showed that the generating function of orbifold elliptic genera of
symmetric orbifolds can be written as an infinite product. We show that there
exists a geometric factorization on space level behind this infinite product
formula, and we do this in the much more general framework of orbifold
mapping spaces, where factors in the infinite product correspond to finite
connected coverings of domain spaces whose fundamental groups are not
necessarily abelian. From this formula, a concept of geometric Hecke operators
for functors emerges. This is a nonabelian geometric generalization of the
usual Hecke operators. We show that these generalized Hecke operators
indeed satisfy the identity of the usual Hecke operators for the case of
–dimensional
tori.
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Keywords
Hecke operators, orbifold elliptic genus, orbifold Euler
characteristic, orbifold mapping space, orbifold loop
space, symmetric orbifold, wreath product orbifold
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Mathematical Subject Classification 2000
Primary: 55N20, 55N91
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Publication
Received: 1 July 2008
Revised: 20 February 2009
Accepted: 26 February 2009
Published: 30 March 2009
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