Tokuyama-type formulas for characters of type B

We obtain explicit formulas for the product of a deformed Weyl denominator with the character of an irreducible representation of the spin group Spin 2 r +1 (C), which is an analogue of the formulas of Tokuyama for Schur polynomials and Hamel–King for characters of symplectic groups. To give these,...

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Bibliographic Details
Published in:Israel journal of mathematics 2016-10, Vol.216 (2), p.617-655
Main Authors: Friedberg, Solomon, Zhang, Lei
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Deformation
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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Summary:We obtain explicit formulas for the product of a deformed Weyl denominator with the character of an irreducible representation of the spin group Spin 2 r +1 (C), which is an analogue of the formulas of Tokuyama for Schur polynomials and Hamel–King for characters of symplectic groups. To give these, we start with a symplectic group and obtain such characters using the Casselman–Shalika formula. We then analyze this using objects which are naturally attached to the metaplectic double cover of an odd orthogonal group, which also has dual group Spin 2 r +1 (C).
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-016-1422-6