Symmetric functions Lecture Notes
نویسنده
چکیده
Tableaux Let λ be a partition and let μ = (μ1, . . . , μn) ∈ Z≥0 be a sequence of nonnegative integers. A column strict tableau of shape λ and weight μ is a filling of the boxes of λ with μ1 1s, μ2 2s, . . ., μn ns, such that (a) the rows are weakly increasing from left to right, (b) the columns are strictly increasing from top to bottom. If p is a column strict tableau write shp(p) and wt(p) for the shape and the weight of p so that
منابع مشابه
Symmetric functions: Definition of the Schur functions Lecture Notes
1. The GL n (C) case The following fundamental example motivates the general case.
متن کاملTraceless Symmetric Tensor Approach to Legendre Polynomials and Spherical Harmonics
In these notes I will describe the separation of variable technique for solving Laplace’s equation, using spherical polar coordinates. The solutions will involve Legendre polynomials for cases with azimuthal symmetry, and more generally they will involve spherical harmonics. I will construct these solutions using traceless symmetric tensors, but in Lecture Notes 8 I describe how the solutions i...
متن کاملH. Upmeier
1. S. GiNDiKrN, 'Analysis on homogeneous domains', Russian Math. Surveys 19 (1964) 1-89. 2. M. KOECHER, 'An elementary approach to bounded symmetric domains', Lecture Notes, Rice University, 1969. 3. O. Loos, 'Bounded symmetric domains and Jordan pairs', Lecture Notes, University of California, Irvine, 1977. 4. A. UNTERBERGER and H. UPMEIER, Pseudodifferential analysis on symmetric cones (CRC-P...
متن کاملIntroductions to Symmetric Polynomials and Symmetric Functions
Symmetric polynomials and symmetric functions are ubiquitous in mathematics and mathematical physics. For example, they appear in elementary algebra (e.g. Viete’s Theorem), representation theories of symmetric groups and general linear groups over C or finite fields. They are also important objects to study in algebraic combinatorics. Via their close relations with representation theory, the th...
متن کاملFactors affecting students tendency of Univercity students to Lecture Notes
Introduction: Many studies detected factors contributing to the students’ tendency to lecture notes. This study aimed at evaluating the factors affecting students tendency to lecture notes in Hormozgan University of Medical Sciences. Methods: In this descriptive study, 179 students from medicine, nursing & midwifery, health, and Paramedicine schools were selected through stratified random...
متن کاملSymmetric functions Lecture Notes: Schur functions
If f ∈ Z[Xn]n and g ∈ An then fg ∈ An and so An is a Z[Xn]n -module. The symmetric group Sn acts on Z≥0 by permuting the coordinates. If Z = {(γ1, . . . , γ) | γi ∈ Z}, P = {(γ1, . . . , γ) ∈ Z | γ1 ≥ γ2 ≥ · · · ≥ γn}, and P = {(γ1, . . . , γ) ∈ Z | γ1 > γ2 > · · · > γn}, then P is a set of representatives of the orbits of the Sn action on Z and the map defined by P −→ P λ 7−→ λ+ ρ where ρ = (n...
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 2004