Tohoku Mathematical Journal
2003

June
SECOND SERIES VOL. 55, NO. 2

Tohoku Math. J.
55 (2003), 157-173

Title TWINING CHARACTERS AND KOSTANT'S HOMOLOGY FORMULA

Author Satoshi Naito

(Received April 17, 2001)
Abstract. Let $\mathfrak{g}$ be a symmetrizable generalized Kac-Moody algebra and $\mathfrak{n}_-$ the sum of all its negative root spaces. We obtain a formula for the twining characters of the Lie algebra homology modules of $\mathfrak{n}_-$ with coefficients in the irreducible highest weight $\mathfrak{g}$-module $L(\Lambda)$ of symmetric, dominant integral highest weight $\Lambda$. This formula gives a new (and convincing) proof of the formula for the twining character of $L(\Lambda)$ above.

2000 Mathematics Subject Classification. Primary 17B67; Secondary 17B10, 17B55.

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