n-SCHUR FUNCTIONS AND DETERMINANTS ON AN INFINITE GRASSMANNIAN
نویسنده
چکیده
Abstract. A set of functions is defined which is indexed by a positive integer n and partitions of integers. The case n = 1 reproduces the standard Schur polynomials. These functions are seen to arise naturally as a determinant of an action on the frame bundle of an infinite grassmannian. This fact is well known in the case of the Schur polynomials (n = 1) and has been used to decompose the τ -functions of the KP hierarchy as a sum. In the same way, the new functions introduced here (n > 1) are used to expand quotients of τ -functions as a sum with Plücker coordinates as coefficients.
منابع مشابه
Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions, and Schur Functions
In this paper we derive many infinite families of explicit exact formulas involving either squares or triangular numbers, two of which generalize Jacobi’s 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. In fact, we similarly generalize to infinite families all of Jacobi’s explicitly stated degree 2, 4, 6, 8 Lambert series expansions of classical t...
متن کاملDeterminantal Forms for Symplectic and Orthogonal Schur Functions
Symplectic and orthogonal Schur functions can be defined combinatorially in a manner similar to the classical Schur functions. This paper demonstrates that they can also be expressed as determinants. These determinants are generated using planar decompositions of tableaux into strips and the equivalence of these determinants to symplectic or orthogonal Schur functions is established by Gessel-V...
متن کاملPfaffians 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...
متن کاملPlücker Relations on Schur Functions
We present a set of algebraic relations among Schur functions which are a multi-time generalization of the “discrete Hirota relations” known to hold among the Schur functions of rectangular partitions. We prove the relations as an application of a technique for turning Plücker relations into statements about Schur functions and other objects with similar definitions as determinants. We also giv...
متن کاملSchur positivity of skew Schur function differences and applications to ribbons and Schubert classes
Some new relations on skew Schur function differences are established both combinatorially using Schützenberger’s jeu de taquin, and algebraically using Jacobi-Trudi determinants. These relations lead to the conclusion that certain differences of skew Schur functions are Schur positive. Applying these results to a basis of symmetric functions involving ribbon Schur functions confirms the validi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998