Alcove walks and nearby cycles on affine flag manifolds

Journal of Algebraic Combinatorics ◽

10.1007/s10801-007-0063-6 ◽

2007 ◽

Vol 26 (4) ◽

pp. 415-430 ◽

Author(s):

Ulrich Görtz

Keyword(s):

Flag Manifolds ◽

Nearby Cycles ◽

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Bounds on Weights of Nearby Cycles and Wakimoto Sheaves on Affine Flag Manifolds

manuscripta mathematica ◽

10.1007/s00229-006-0005-y ◽

2006 ◽

Vol 120 (4) ◽

pp. 347-358 ◽

Author(s):

Ulrich Görtz ◽

Thomas J. Haines

Keyword(s):

Flag Manifolds ◽

Nearby Cycles ◽

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Equivariant $K$ -theory of affine flag manifolds and affine Grothendieck polynomials

Duke Mathematical Journal ◽

10.1215/00127094-2009-032 ◽

2009 ◽

Vol 148 (3) ◽

pp. 501-538 ◽

Author(s):

Masaki Kashiwara ◽

Mark Shimozono

Keyword(s):

Flag Manifolds ◽

K Theory ◽

Affine Flag ◽

Grothendieck Polynomials

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The geometry of fixed point varieties on affine flag manifolds

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-99-02295-3 ◽

1999 ◽

Vol 352 (5) ◽

pp. 2087-2119 ◽

Author(s):

Daniel S. Sage

Keyword(s):

Fixed Point ◽

Flag Manifolds ◽

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The Jordan-Hölder series for nearby cycles on some Shimura varieties and affine flag varieties

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crelle.2007.063 ◽

2007 ◽

Vol 2007 (609) ◽

Author(s):

Ulrich Görtz ◽

Thomas J Haines

Keyword(s):

Shimura Varieties ◽

Flag Varieties ◽

Nearby Cycles ◽

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Double Affine Hecke Algebras and Affine Flag Manifolds, I

Affine Flag Manifolds and Principal Bundles ◽

10.1007/978-3-0346-0288-4_9 ◽

2010 ◽

pp. 233-289 ◽

Author(s):

Michela Varagnolo ◽

Eric Vasserot

Keyword(s):

Hecke Algebras ◽

Flag Manifolds ◽

Double Affine Hecke Algebras ◽

Affine Hecke Algebras ◽

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Fixed point varieties on affine flag manifolds

Israel Journal of Mathematics ◽

10.1007/bf02787119 ◽

1988 ◽

Vol 62 (2) ◽

pp. 129-168 ◽

Author(s):

D. Kazhdan ◽

G. Lusztig

Keyword(s):

Fixed Point ◽

Flag Manifolds ◽

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The dimension of the fixed point set on affine flag manifolds

Mathematical Research Letters ◽

10.4310/mrl.1996.v3.n2.a5 ◽

1996 ◽

Vol 3 (2) ◽

pp. 185-189 ◽

Author(s):

Roman Bezrukavnikov

Keyword(s):

Fixed Point ◽

Flag Manifolds ◽

Fixed Point Set ◽

Point Set ◽

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Instanton counting via affine Lie algebras. I. Equivariant 𝐽-functions of (affine) flag manifolds and Whittaker vectors

CRM Proceedings and Lecture Notes - Algebraic Structures and Moduli Spaces ◽

10.1090/crmp/038/04 ◽

2004 ◽

pp. 113-132 ◽

Author(s):

Alexander Braverman

Keyword(s):

Lie Algebras ◽

Flag Manifolds ◽

Affine Lie Algebras ◽

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Monodromic systems on affine flag manifolds

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1994.0058 ◽

1994 ◽

Vol 445 (1923) ◽

pp. 231-246 ◽

Keyword(s):

Positive Characteristic ◽

Flag Manifold ◽

Flag Manifolds ◽

Modular Representations ◽

Affine Weyl Group ◽

Dual Affine ◽

Substantial Progress ◽

Affine Hecke Algebras ◽

Field Of Positive Characteristic ◽

There has been recently substantial progress in the programme of expressing the characters of irreducible modular representations of a semisimple group over a field of positive characteristic in terms of combinatorics of affine Hecke algebras (see Andersen et al . 1992; Kazhdan & Lusztig 1979). This paper is a further contribution to this programme: I explain why in the non-simply laced case, the ‘dual’ affine Weyl group is needed and why in this case it is necessary to use monodromic systems (certain local systems defined on subvarieties of a line bundle) over an affine flag manifold.

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Errata - Monodromic systems on affine flag manifolds

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1995.0113 ◽

1995 ◽

Vol 450 (1940) ◽

pp. 731-732 ◽

Keyword(s):

Flag Manifolds ◽

Section 8 ◽

Proc. R. Soc. Lond. A 445, 231-246 (1994) Monodromic systems on affine flag manifolds By George Lusztig Section 8 contains a blunder; I am indebted to Alexander Kirillov Jr for pointing this out to me. In the second sentence of 8.2 on p. 244, replace ς=exp(π√-1/ (σ + g )) by ς = exp(π√-1/ D (σ + g )). The subsequent sentences of 8.2 and all of 8.3 should be deleted. Replace the text of 8.4 on p. 245, starting with the second sentence, by the following text.

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