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


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.


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

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T. J ́ozefiak, Characters of projective representations of symmetric groups, Expo. Math. 7 (1989), 193–247. (Google Scholar)

I. G. Macdonald, Symetric functions and Hall polynomilas, 2nd edition, Oxford University Press, Oxford, 1995. (Google Scholar)

A. O. Morris, The spin representation of the symetric group, Canad. J. Math. 17 (1965), 543–549. (Google Scholar)

B. E. Sagan, Shifted tableaux, Schur Q-functions and a conjecture of R. Stanley, J. Combin. Theory Ser. A 45 (1987), 62–103. (Google Scholar)

B. E. Sagan, The symmetric group, Springer-Verlag, New York, 2000. (Google Scholar)

I. Schur, U ̈ber die Darstellung der symmetischen und der alternierenden Gruppe durch gebrochene lineare Substitutionen, J. Reine Angew: Math. 131(1911), 155–250. (Google Scholar)

J. R. Stembridge, Shifted tableaux and projective representations of symmetric groups, Advances in Math. 74 (1989), 87–134. (Google Scholar)

J. R. Stembridge, On symmetric functions and spin characters of Sn, Topics in algebra, Banach Center Publ. 26 (1990), part 2, Polish Scientific Publishers, 433–453. (Google Scholar)

D. E. White, Orthogonality of the characters of Sn, J. Combin. Theory (A), 40 (1985), 265–275. (Google Scholar)

D. E. White, A bijection proving orthogonality of the characters of Sn, Advances in Math. 50 (1983), 160–186. (Google Scholar)

D. R. Worley, A theory of Shifted Young Tableaux, Ph. D. thesis, M.I.T., 1984. (Google Scholar)


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