Grassmannian

We prove the strong Macdonald conjecture of Hanlon and Feigin for reductive groups G. In a geometric reformulation, we show that the Dolbeault cohomology H q (X; Ωp ) of the loop Grassmannian X is freely generated by de Rham’s forms on the disk coupled to the indecomposables of H • (BG). Equating the two Euler characteristics gives an identity, independently known to Macdonald [M], which generalises Ramanujan’s 1 ψ1 sum. For simply laced root systems at level 1, we also find a ‘strong form’ of Bailey’s 4 ψ4 sum. ...

47p dontetvui 17-01-2013 59 7   Download

We describe a Schubert induction theorem, a tool for analyzing intersections on a Grassmannian over an arbitrary base ring. The key ingredient in the proof is the Geometric Littlewood-Richardson rule of [V2]. As applications, we show that all Schubert problems for all Grassmannians are enumerative over the real numbers, and sufficiently large finite fields. We prove a generic smoothness theorem as a substitute for the Kleiman-Bertini theorem in positive characteristic.

25p noel_noel 17-01-2013 50 5   Download

We study the Radon transform Rf of functions on Stiefel and Grassmann manifolds. We establish a connection between Rf and G˚ arding-Gindikin fractional integrals associated to the cone of positive definite matrices. By using this connection, we obtain Abel-type representations and explicit inversion formulae for Rf and the corresponding dual Radon transform. We work with the space of continuous functions and also with Lp spaces.

36p tuanloccuoi 04-01-2013 66 9   Download

Characteristic cohomology classes, defined in modulo 2 coefficients by Stiefel [26] and Whitney [28] and with integral coefficients by Pontrjagin [24], make up the primary source of first-order invariants of smooth manifolds. When their utility was first recognized, it became an obvious goal to study the ways in which they admitted extensions to other categories, such as the categories of topological or PL manifolds; perhaps a clean description of characteristic classes for simplicial complexes could even give useful computational techniques.

25p tuanloccuoi 04-01-2013 60 6   Download

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Geometric Properties of Grassmannian Frames for R2 and R3

17p dauphong20 11-03-2012 42 4   Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: Affine partitions and affine Grassmannians...

45p thulanh7 03-10-2011 60 4   Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: Dissimilarity vectors of trees are contained in the tropical Grassmannian...

7p thulanh8 19-09-2011 56 2   Download