A new formula for Pfaffian-type Segal-Sugawara vector

2013/09/08 by Natasha Rozhkovskaya, Rozhkovskaya, Natasha
Mathematics · #17B35 #17B67 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #math.CO #math.QA #msc:17B35 #msc:17B67

paper · pdf · doi:10.48550/arxiv.1309.1958

14 pages

arxiv created 2013/09/08 · arxiv updated 2013/09/10

Abstract

A combinatorial formula for Pfaffian for the universal enveloping algebra of the affine Kac - Moody algebra of even orthogonal Lie algebra is proved. It allows easily to compute the image of this Segal-Sugawara vector under the Harish-Chandra homomorphism and to deduce formulas for classical Pfaffian of universal enveloping algebra of the even orthogonal Lie algebra.

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