Spin Hurwitz theory and Miwa transform for the Schur Q-functions

Schur Q-functions and spin characters of symmetric groups I

In a classic paper, I. Schur [6] introduced a class of symmetric functions, now called Schur Qfunctions, in order to determine the irreducible spin (projective) characters of symmetric groups. In the case of the ordinary characters of symmetric groups, going back to the early work of D. E. Littlewood and A. R. Richardson [3], the corresponding Schur functions have been used to give useful combi...

Multiplying Schur Q-functions

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...

The Horn Recursion for Schur P - and Q - Functions : Extended

A consequence of work of Klyachko and of Knutson-Tao is the Horn recursion to determine when a Littlewood-Richardson coefficient is non-zero. Briefly, a LittlewoodRichardson coefficient is non-zero if and only if it satisfies a collection of Horn inequalities which are indexed by smaller non-zero Littlewood-Richardson coefficients. There are similar Littlewood-Richardson numbers for Schur P and...

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...