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LITTLEWOOD'S MULTIPLE FORMULA FOR SPIN CHARACTERS OF SYMMETRIC GROUPS

Published online by Cambridge University Press:  06 March 2002

HIROSHI MIZUKAWA  and
HIRO-FUMI YAMADA
HIROSHI MIZUKAWA
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan; mzh@math.sci.hokudai.ac.jp
HIRO-FUMI YAMADA
Affiliation:
Department of Mathematics, Okayama University, Okayama 700-8530, Japan; yamada@math.okayama-u.ac.jp
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Abstract

This paper deals with some character values of the symmetric group Sn as well as its double cover S˜n.

Let χλ(ρ) be the irreducible character of Sn, indexed by the partition λ and evaluated at the conjugacy class ρ. Comparing the character tables of S2 and S4, one observes that

for ρ = (2), 2ρ = (4) and ρ = (12), 2ρ = (22). A number of such observations lead to what we call Littlewood's multiple formula (Theorem 1.1). This formula appears in Littlewood's book [2]. We include a proof that is based on an ‘inflation’ of the variables in a Schur function. This is different from one given in [2], and we claim that it is more complete than the one given there.

Our main objective is to obtain the spin character version of Littlewood's multiple formula (Theorem 2.3).

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 65 , Issue 1 , February 2002 , pp. 1 - 9
Copyright
2002 London Mathematical Society

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