Noncommutative pfaffians and representations

2011/11/23 by D. V. Artamonov, Artamonov, D. V., V. A. Goloubeva +1 · 1 citation
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1111.5521

24 pages, several proofs are improved

arxiv created 2012/05/21 · arxiv updated 2012/05/22

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.

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