Schur \(Q\)-functions and spin characters of symmetric groups. I
type: Item
instance of: scholarly article
title: Schur \(Q\)-functions and spin characters of symmetric groups. I
zbMATH Open document ID: 0867.05082
author: Yanyan Li
published in: The Electronic Journal of Combinatorics
publication date: 1996-07-21T00:00:00Z
full work available at URL: https://eudml.org/doc/119124
full work available at URL: R20
review text: The main theorem of this paper is a combinatorial formula for the spin character (or projective character) for the symmetric group \(\zeta^\lambda_\pi\). A simpler formula for the case when \(\lambda\) has two parts is also given. These formulae are stated in terms of objects called ``complete separations of the partition \(\pi\)'' corresponding with a composition. A complete separation of \(\pi\) is an ordered set-partition of the numbers in \(\pi\) such that the block sums are determined by the composition. The character formulas are proved using several identities for Schur \(Q\)-functions. In addition to the authors' proofs, Theorems 3.5 and 2.2 have appeared in Section 1 of an article by \textit{P. Pragacz} [Algebro-geometric applications of Schur \(S\)- and \(Q\)-polynomials, Topics in invariant theory (Paris 1989/1990), Lect. Notes Math. 1478, 130-191 (1991; Zbl 0783.14031)].
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 05E15
zbMATH DE Number: 907659
zbMATH Keywords: Schur \(Q\)-functions
zbMATH Keywords: spin character
zbMATH Keywords: projective character
zbMATH Keywords: symmetric group
zbMATH Keywords: partition
reviewed by: Sara Billey
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 907659