Bilinear expansion of Schur functions in Schur Q-functions: A fermionic approach

Multiplying Schur Q-functions

Interpolation Analogues of Schur Q-functions

We introduce interpolation analogues of Schur Q-functions — the multiparameter Schur Q-functions. We obtain for them several results: a combinatorial formula, generating functions for one-row and two-rows functions, vanishing and characterization properties, a Pieri-type formula, a Nimmo-type formula (a relation of two Pfaffians), a Giambelli-Schur-type Pfaffian formula, a determinantal formula...

Pfaffians and Determinants for Schur Q-Functions

Schur Q-functions were originally introduced by Schur in relation to projective representations of the symmetric group and they can be defined combinatorially in terms of shifted tableaux. In this paper we describe planar decompositions of shifted tableaux into strips and use the shapes of these strips to generate pfaffi.ans and determinants that are equal to Schur Q-functions. As special cases...

Schur Functions

Editorial comments. The Schur functions sλ are a special basis for the algebra of symmetric functions Λ. They are also intimately connected with representations of the symmetric and general linear groups. In what follows we will give two alternative definitions of these functions, show how they are related to other symmetric function bases, explicitly describe their connection with representati...

Products of Schur and Factorial Schur Functions

The product of any finite number of Schur and factorial Schur functions can be expanded as a Z[y]-linear combination of Schur functions. We give a rule for computing the coefficients in such an expansion which generalizes the classical Littlewood-Richardson rule.