Grassmannian

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Grassmannian

[¦gräs¦man·ē·ən]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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The lectures cover perverse sheaves and the topology of algebraic varieties, an introduction to affine Grassmannians and the geometric Satake equivalence, Springer theories and orbital integrals, perverse sheaves and fundamental lemmas, K-theory computations in enumerative geometry, and perverse sheaves on instanton moduli spaces.
Skinner, "Dual superconformal invariance, momentum twistors and Grassmannians," Journal of High Energy Physics, vol.
It is also worth mentioning that in [3] Buch obtained the Littlewood-Richardson rule for the structure constants of Grothendieck polynomials [G.sub.[lambda]](x), and hence the Schubert structure constants of the K-theory of Grassmannians (see also the paper [9] by Ikeda-Shimazaki for another proof) For the equivariant K-theory of Grassmannians (or equivalently for [G.sub.[lambda]](x|b)), the structure constants were determined by Pechenik and Yong in [20] by introducing a new combinatorial object called genomic tableaux.
Riepel, Categorical Lagrangian Grassmannians and Brauer-Picard groups of pointed fusion categories, J.
Total positivity for cominuscule Grassmannians. New York J.
[BKT03] Anders Skovsted Buch, Andrew Kresch, and Harry Tamvakis, Gromov-Witten invariants on Grassmannians, J.
LIM, Quasi-Newton methods on Grassmannians and multilinear approximations of tensors, SIAM J.
Grassmannians, moduli spaces and vector bundles; proceedings.
For example, from the usual representation of SLn(R) on C", one obtains actions on the parameter spaces of linear subspaces, that is, Grassmannians [Gr.sub.K]([C.sup.n]) of k-dimensional subspaces of [C.sup.n], flag manifolds [F.sub.1:::k]([C.sup.n]) and so on.
Drawn from lectures at a program held in 1999 in Taiwan's National Center for Theoretical Sciences, the topics include isothermic surfaces in terms of conformal geometry, Clifford algebras and integrable systems, introductions to homological geometry, isoparametric submanifolds and a Chevalley-type restriction theorem, a gauge-theoretic approach to harmonic maps and subspaces in Moduli spaces, and Schrodinger flows on Grassmannians.
This is the first contribution to the rigidity question for an important class of irreducible Hermitian symmetric spaces, the complex Grassmannians. Indeed, [Q.sub.4] may be identified with the Grassmannian of complex 2-planes in [C.sup.4].