Related Experiment Video
Updated: Aug 9, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
Published on: July 19, 2016
T-equivariant K-theory of generalized flag varieties
Abstract:
Let G be a Kac-Moody group with Borel subgroup B and compact maximal torus T. Analogous to Kostant and Kumar [Kostant, B. & Kumar, S. (1986) Proc. Natl. Acad. Sci. USA 83, 1543-1545], we define a certain ring Y, purely in terms of the Weyl group W (associated to G) and its action on T. By dualizing Y we get another ring Psi, which, we prove, is "canonically" isomorphic with the T-equivariant K-theory K(T)(G/B) of G/B. Now K(T)(G/B), apart from being an algebra over K(T)(pt.) approximately A(T), also has a Weyl group action and, moreover, K(T)(G/B) admits certain operators {D(w)}w[unk]W similar to the Demazure operators defined on A(T). We prove that these structures on K(T)(G/B) come naturally from the ring Y. By "evaluating" the A(T)-module Psi at 1, we recover K(G/B) together with the above-mentioned structures. We believe that many of the results of this paper are new in the finite case (i.e., G is a finite-dimensional semisimple group over C) as well.
Related Concept Videos
Fundamental Theorem of Algebra
Torsion in Vector Calculus
Vector Forms of Green’s Theorem
Extended Versions of Green’s Theorem
Conservative Vector Fields
Curvature and Its Interpretation
