Takashi Hashimoto
Published 2006-02-03, updated 2006-04-03Version 2
It is known that the universal enveloping algebra of the orthogonal Lie algebra of size even has a central element expressed in terms of Pfaffian of a certain matrix alternating along the anti-diagonal (which we call anti-alternating for short) whose entries are in the univerasal enveloping algebra. In this paper, we establish minor summation formulae of Pfaffian for the noncommutative anti-alternating matrix, as well as for commutative anti-alternating matrix. As an application, we show that the eigenvalues on the highest weight modules of the central element given by the Pfaffian can be easily computed.
Comments: version 1.1(corrected typos and added a reference), 17 pages, no figures
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