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Multiplicity Free Expansions of Schur P-Functions
Kristin M. Shaw, Stephanie van Willigenburg
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
{krishaw, steph}@math.ubc.ca
Annals of Combinatorics 11 (1) p.69-77 March, 2007
AMS Subject Classification: 05E05, 05A17, 05A19, 05E10
Abstract:
After deriving inequalities on coefficients arising in the expansion of a Schur Pfunction in terms of Schur functions we give criteria for when such expansions are multiplicity free. From here we study the multiplicity of an irreducible spin character of the twisted symmetric group in the product of a basic spin character with an irreducible character of the symmetric group, and determine when it is multiplicity free.
Keywords: multiplicity free, Schur functions, Schur P-functions, spin characters, staircase partitions

References:

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2. I.G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd Ed., Oxford University Press, Oxford, 1995.

3. J. Stembridge, Shifted tableaux and the projective representations of symmetric groups, Adv. Math. 74 (1989) 87-134.

4. J. Stembridge, Multiplicity-free products of Schur functions, Ann. Combin. 5 (2001) 113- 121.