Combinatorial interpretations of the orthogonality relations for spin characters of Sn
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In 1911 Schur[6] derived degree and character formulas for projective representations of the symmetric groups remarkably similar to the corresponding formulas for ordinary representations. Morris[3] derived a recurrence for evaluation of spin characters and Stembridge\cite[8] gave a combinatorial reformulation for Morris' recurrence. In this paper we give combinatorial interpretations for the orthogonality relations of spin characters based on Stembridge's combinatorialreformulation for Morris' rule.
Abstract
In 1911 Schur[6] derived degree and character formulas for projective representations of the symmetric groups remarkably similar to the corresponding formulas for ordinary representations. Morris[3] derived a recurrence for evaluation of spin characters and Stembridge\cite[8] gave a combinatorial reformulation for Morris' recurrence. In this paper we give combinatorial interpretations for the orthogonality relations of spin characters based on Stembridge's combinatorialreformulation for Morris' rule.
참고문헌 (11)
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- J. R. Stembridge, "Shifted tableaux and projective representations of symmetric groups", Advances in Math, 74, pp.87~134 (1989)
- J. R. Stembridge, "On symmetric functions and spin characters of Sn, Topics in algebra", pp.433~453 (1990), Polish Scientific Publishers
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