The Polynomial Behavior of Weight Multiplicities for the Affine Kac-moody Algebras
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چکیده
We prove that the multiplicity of an arbitrary dominant weight for an integrable highest weight representation of the affine Kac-Moody algebra A (1) r is a polynomial in the rank r. In the process we show that the degree of this polynomial is less than or equal to the depth of the weight with respect to the highest weight. These results allow weight multiplicity information for small ranks to be transferred to arbitrary ranks. Supported in part by NSF Grants #DMS-9300523 and #DMS-9622447 Supported by the Non-directed Research Fund, Korea Research Foundation, 1996 Supported in part by NSA/MSP Grant #MDA904-96-1-0013 1991 Mathematics Subject Classifications: 17B67, 17B65 Typeset by AMS-TEX 1
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تاریخ انتشار 1998