Noncommutative pfaffians and representations

Abstract

Noncommutative pfaffians associated with an orthogonal algebra are some special elements of the universal enveloping algebra. In the paper it is suggested to use some pfaffians as raising operators. The images of these pfaffians in the Mickelson-Zhelobenko algebra are calculated. It allows to find a place of pfaffians among other raising operators. As a byproduct the action of the pfaffians on the Gelfand-Tsetlin-Molev bases is found. The action of pfaffians in the tensor realization of representation is considered in the appendix.

24 pages, several proofs are improved

References in corpus (3)

• A Basis for Representations of Symplectic Lie Algebras
• Weight bases of Gelfand-Tsetlin type for representations of classical Lie algebras
• A central element in the universal enveloping algebra of type D_n via minor summation formula of Pfaffians

Cited by in corpus (1)

• Decomplexification of the Capelli identities and holomorphic factorization