Noncommutative schur functions and their applications
نویسندگان
چکیده
We develop a theory of Schur functions in noncommuting variables, assuming commutation relations that are satissed in many well-known associative algebras. As an application of our theory, we prove Schur-positivity and obtain generalized Littlewood-Richardson and Murnaghan-Nakayama rules for a large class of symmetric functions, including stable Schubert and Grothendieck polynomials.
منابع مشابه
Noncommutative irreducible characters of the symmetric group and noncommutative Schur functions
In the Hopf algebra of symmetric functions, Sym, the basis of Schur functions is distinguished since every Schur function is isomorphic to an irreducible character of a symmetric group under the Frobenius characteristic map. In this note we show that in the Hopf algebra of noncommutative symmetric functions, NSym, of which Sym is a quotient, the recently discovered basis of noncommutative Schur...
متن کاملA Murnaghan-Nakayama rule for noncommutative Schur functions
We prove a Murnaghan-Nakayama rule for noncommutative Schur functions introduced by Bessenrodt, Luoto and van Willigenburg. In other words, we give an explicit combinatorial formula for expanding the product of a noncommutative power sum symmetric function and a noncommutative Schur function in terms of noncommutative Schur functions. In direct analogy to the classical Murnaghan-Nakayama rule, ...
متن کاملSkew Quasisymmetric Schur Functions and Noncommutative Schur Functions
Recently a new basis for the Hopf algebra of quasisymmetric functions QSym, called quasisymmetric Schur functions, has been introduced by Haglund, Luoto, Mason, van Willigenburg. In this paper we extend the definition of quasisymmetric Schur functions to introduce skew quasisymmetric Schur functions. These functions include both classical skew Schur functions and quasisymmetric Schur functions ...
متن کاملNoncommutative Monomial Symmetric Functions
This presentation will introduce noncommutative analogs of monomial symmetric functions (and their dual, forgotten symmetric functions). In analogy to the classical theory, expansion of ribbon Schur functions in this basis in nonnegative. Moreover, one can define fundamental noncommutative symmetric functions by analogy with quasi-symmetric theory. The expansion of ribbon Schur functions in thi...
متن کاملOperators on Compositions and Generalized Skew Pieri Rules
Using operators on compositions we develop further both the theory of quasisymmetric Schur functions and of noncommutative Schur functions. By establishing relations between these operators, we show that the posets of compositions arising from the right and left Pieri rules for noncommutative Schur functions can each be endowed with both the structure of dual graded graphs and dual filtered gra...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Mathematics
دوره 306 شماره
صفحات -
تاریخ انتشار 1998