. A G ] 2 9 Ju n 20 03 THE HODGE STAR OPERATOR ON SCHUBERT FORMS
نویسنده
چکیده
Let X = G/P be a homogeneous space of a complex semisimple Lie group G equipped with a hermitian metric. We study the action of the Hodge star operator on the space of harmonic differential forms on X. We obtain explicit combinatorial formulas for this action when X is an irreducible hermitian symmetric space of compact type.
منابع مشابه
Operator-valued tensors on manifolds
In this paper we try to extend geometric concepts in the context of operator valued tensors. To this end, we aim to replace the field of scalars $ mathbb{R} $ by self-adjoint elements of a commutative $ C^star $-algebra, and reach an appropriate generalization of geometrical concepts on manifolds. First, we put forward the concept of operator-valued tensors and extend semi-Riemannian...
متن کاملPolynomial Histopolation, Superconvergent Degrees of Freedom, and Pseudospectral Discrete Hodge Operators
We show that, given a histogram with n bins—possibly non-contiguous or consisting of single points—there exists a unique polynomial histopolant (polynomial of order n with bin averages equal to the histogram’s). We also present histopolating cardinal functions for histograms with contiguous bins. The Hodge star operator from the theory of differential forms is the mapping which puts kand (d − k...
متن کاملar X iv : a lg - g eo m / 9 60 20 19 v 1 2 7 Fe b 19 96 FORMULAS FOR LAGRANGIAN AND ORTHOGONAL DEGENERACY LOCI ; The Q̃ - Polynomials Approach
Introduction 1. Schubert subschemes and their desingularizations. 2. Isotropic Schubert calculus and the class of the diagonal. 3. Subbundles intersecting an n-subbundle in dim > k. 4. Q̃-polynomials and their properties. 5. Divided differences and isotropic Gysin maps; orthogonality of Q̃-polynomials. 6. Single Schubert condition. 7. Two Schubert conditions. 8. An operator proof of Proposition 3...
متن کاملm at h . D G ] 2 4 Ju n 20 04 CANONICAL EQUIVARIANT EXTENSIONS USING CLASSICAL HODGE THEORY
Lin and Sjamaar have used symplectic Hodge theory to obtain canonical equivariant extensions for Hamiltonian actions on closed symplectic manifolds that have the strong Lefschetz property. Here we obtain canonical equivariant extensions much more generally by means of classical Hodge theory.
متن کامل. D G ] 2 4 Ju n 20 04 CANONICAL EQUIVARIANT EXTENSIONS USING CLASSICAL HODGE THEORY
Lin and Sjamaar have used symplectic Hodge theory to obtain canonical equivariant extensions for Hamiltonian actions on closed symplectic manifolds that have the strong Lefschetz property. Here we obtain canonical equivariant extensions much more generally by means of classical Hodge theory.
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 2008