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A combinatorial identity for the derivative of a theta series of a finite type root lattice

Published online by Cambridge University Press:  22 January 2016

Satoshi Naito
Satoshi Naito*
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba Ibaraki, 305-8571, Japan, naito@math.tsukuba.ac.jp
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Abstract

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Let be a (not necessarily simply laced) finite-dimensional complex simple Lie algebra with the Cartan subalgebra and Q ⊂ * the root lattice. Denote by ΘQ(q) the theta series of the root lattice Q of . We prove a curious “combinatorial” identity for the derivative of ΘQ(q), i.e. for by using the representation theory of an affine Lie algebra.

Keywords

05A1505A3017B67
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 172 , 2003 , pp. 1 - 30
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2003

References

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