Korean J. Math.  Vol 22, No 2 (2014)  pp.325-337
DOI: https://doi.org/10.11568/kjm.2014.22.2.325

Combinatorial interpretations of the orthogonality relations for spin characters of $\tilde{S_n}$

Jaejin Lee

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[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 combinatorial reformulation for Morris' rule.


Keywords


partition, shifted rimhook tableaux, spin character, symmetric function, $P$-function, $Q$-function, orthogonality relation

Subject classification

05E10

Sponsor(s)



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References


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