Affine Flag Manifolds and Principal Bundles - download pdf or read online

By Alexander Schmitt

ISBN-10: 3034602871

ISBN-13: 9783034602877

ISBN-10: 303460288X

ISBN-13: 9783034602884

Affine flag manifolds are countless dimensional models of standard gadgets comparable to Gra?mann forms. The ebook good points lecture notes, survey articles, and learn notes - in line with workshops held in Berlin, Essen, and Madrid - explaining the importance of those and similar gadgets (such as double affine Hecke algebras and affine Springer fibers) in illustration conception (e.g., the speculation of symmetric polynomials), mathematics geometry (e.g., the elemental lemma within the Langlands program), and algebraic geometry (e.g., affine flag manifolds as parameter areas for central bundles). Novel elements of the speculation of vital bundles on algebraic kinds also are studied within the publication.

Show description

Read Online or Download Affine Flag Manifolds and Principal Bundles PDF

Similar mathematics books

Juan Carlos De Los Reyes's Numerical Pde-Constrained Optimization PDF

This e-book introduces, in an available means, the elemental parts of Numerical PDE-Constrained Optimization, from the derivation of optimality stipulations to the layout of answer algorithms. Numerical optimization tools in function-spaces and their software to PDE-constrained difficulties are conscientiously provided.

Download e-book for kindle: Fixed Point Theory of Parametrized Equivariant Maps by Hanno Ulrich

The 1st a part of this examine monograph discusses basic houses of G-ENRBs - Euclidean Neighbourhood Retracts over B with motion of a compact Lie crew G - and their relatives with fibrations, non-stop submersions, and fibre bundles. It therefore addresses equivariant aspect set topology in addition to equivariant homotopy conception.

Additional resources for Affine Flag Manifolds and Principal Bundles

Example text

5. 6. 31 are σ-conjugate to the identity element. Therefore in the classical case there is no need to introduce the parameter b which we see above. On the other hand, the Lang map G(L) → G(L) is not surjective. In fact, we have seen above that G(L) consists of many σ-conjugacy classes. The usual proof for the surjectivity of the Lang map fails in the setting of ind-schemes: although the differential of the Lang map g → g −1 σ(g) is an isomorphism, one cannot conclude that the map itself is “´etale”.

6. It is expected that in the hyperspecial case, all affine Deligne–Lusztig varieties are equidimensional. 1 in [26] shows that Xμ (b) is equidimensional. The proof relies on a result proved by Mirkovi´c and Vilonen as part of their proof of the geometric Satake isomorphism. More precisely, their results about the intersection cohomology of intersections of U (L)and K-orbits imply that these intersections are equidimensional. For a proof of the relevant fact in positive characteristic, which is what one needs in our situation, see the paper [62] by Ngˆ o and Polo.

2. The σ-conjugacy class can be represented by an element τ ∈ W with (τ ) = 0. We call an element b ∈ G(L) basic, if its σ-conjugacy class is basic. 1). Looking at σ-conjugacy classes from the point of view of Newton strata in the special fiber of a Shimura variety, the basic locus is the unique closed Newton stratum. In the case of the Siegel modular variety, for instance, this is just the supersingular locus. 3. Affine Deligne–Lusztig varieties: the hyperspecial case Similarly as for usual Deligne–Lusztig varieties, we want to consider all elements g which map under a “Lang map” to a fixed double coset.

Download PDF sample

Affine Flag Manifolds and Principal Bundles by Alexander Schmitt

by Jeff

Rated 4.08 of 5 – based on 43 votes