Pfaffian-type Sugawara operators
A. I. Molev
TL;DR
This paper demonstrates that the Pfaffian of a generator matrix for the affine Kac--Moody algebra _{2n} is a Segal--Sugawara vector, completing the set of such vectors in type D with previous constructions.
Contribution
It introduces the Pfaffian as a new Segal--Sugawara vector for _{2n} and completes the set of these vectors in type D.
Findings
Pfaffian of generator matrix is a Segal--Sugawara vector
Complete set of Segal--Sugawara vectors in type D achieved
Connection with earlier Brauer algebra construction
Abstract
We show that the Pfaffian of a generator matrix for the affine Kac--Moody algebra hat o_{2n} is a Segal--Sugawara vector. Together with our earlier construction involving the symmetrizer in the Brauer algebra, this gives a complete set of Segal--Sugawara vectors in type D.
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Taxonomy
TopicsHolomorphic and Operator Theory · Approximation Theory and Sequence Spaces · Advanced Algebra and Logic