Plethystic algebras and vector symmetric functions.

نویسندگان

  • G C Rota
  • J A Stein
چکیده

An isomorphism is established between the plethystic Hopf algebra Pleth(Super[L]) and the algebra of vector symmetric functions. The Hall inner product of symmetric function theory is extended to the Hopf algebra Pleth(Super[L]).

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A computational and combinatorial exposé of plethystic calculus

In recent years, plethystic calculus has emerged as a powerful technical tool for studying symmetric polynomials. In particular, some striking recent advances in the theory of Macdonald polynomials have relied heavily on plethystic computations. The main purpose of this article is to give a detailed explanation of a method for finding combinatorial interpretations of many commonly occurring ple...

متن کامل

POINT DERIVATIONS ON BANACH ALGEBRAS OF α-LIPSCHITZ VECTOR-VALUED OPERATORS

The Lipschitz function algebras were first defined in the 1960s by some mathematicians, including Schubert. Initially, the Lipschitz real-value and complex-value functions are defined and quantitative properties of these algebras are investigated. Over time these algebras have been studied and generalized by many mathematicians such as Cao, Zhang, Xu, Weaver, and others. Let  be a non-emp...

متن کامل

A proof of the q, t-Catalan positivity conjecture

We present here a proof that a certain rational function Cn(q, t) which has come to be known as the “q, t-Catalan” is in fact a polynomial with positive integer coefficients. This has been an open problem since 1994. The precise form of the conjecture is given in the J. Algebraic Combin. 5 (1996), no. 3, 191–244, where it is further conjectured that Cn(q, t) is the Hilbert Series of the Diagona...

متن کامل

Symmetric Functions and Macdonald Polynomials

The ring of symmetric functions Λ, with natural basis given by the Schur functions, arise in many different areas of mathematics. For example, as the cohomology ring of the grassmanian, and as the representation ring of the symmetric group. One may define a coproduct on Λ by the plethystic addition on alphabets. In this way the ring of symmetric functions becomes a Hopf algebra. The Littlewood–...

متن کامل

A Short Proof of a Plethystic

The purpose of this note is to give a short proof of a plethystic generalization of the Murnaghan–Nakayama rule, first stated in [1]. The key step in the proof uses a sign-reversing involution on sequences of bead moves on James’ abacus (see [3, page 78]), inspired by the arguments in [4]. The only prerequisites are the Murnaghan–Nakayama rule and basic facts about plethysms of symmetric functi...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Proceedings of the National Academy of Sciences of the United States of America

دوره 91 26  شماره 

صفحات  -

تاریخ انتشار 1994