A central element in the universal enveloping algebra of type D_n via minor summation formula of Pfaffians
Abstract
Description
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.
version 1.1(corrected typos and added a reference), 17 pages, no figures
version 1.1(corrected typos and added a reference), 17 pages, no figures