Kac-Moody Groups, their Flag Varieties and Representation Theory

By Shrawan Kumar. 2002

906 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b5b45fbf5bb0941481b9650faa010c9917338e2a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Thomas Lam
2. Mark Shimozono
3. Bernard Leclerc
4. C. Geiss
5. J. Schröer
6. Jennifer Morse
7. Luc Lapointe
8. P. Fiebig

In Geometry and Topology

1. Thomas Lam
2. Bernard Leclerc
3. Mark Shimozono
4. C. Geiss
5. J. Schröer
6. Leonardo Constantin Mihalcea
7. H. Naruse
8. Jennifer Morse

In Statistical and Nonlinear Physics

1. C. Geiss
2. J. Schröer
3. Bernard Leclerc
4. P. Fiebig
5. M. Brion
6. Friedrich Wagemann
7. Thomas Lam
8. Aaron D. Lauda

Citations in the corpus

• Simplicity and superrigidity of twin building lattices (2006, background): “Since the origin, Kac-Moody groups (both in their so-called minimal and maximal versions) have been mostly considered as natural analogues of semisimple algebraic groups arising in an infinitedimensional Lie theoretic context (see e.g. [KP83] and [ Kum02 ]).”
• Categorified Quantum sl(2) and Equivariant Cohomology of Iterated Flag Varieties (2008, background): “For a more detailed account in the context of flag varieties see [ 18, Chapter 11.3 ].”
• An upper bound on the exceptional characteristics for Lusztig's character formula (2008, neutral): “For the Kac-Moody versions of the well-known results about Schubert varieties see [ Kum ].”
• Lectures on the Geometry of Flag Varieties (2004, methodology): “For cohomology of line bundles, our approach (based on the KawamataViehweg vanishing theorem) is a variant of that of Kumar; see [39].”
• The spherical Hecke algebra for affine Kac-Moody groups I (2008, neutral): “[10]) that a form Q as above gives rise to a central extension ‹ G of G[t, t−1]: 1→ Gm → ‹ G→ G[t, t−1]→ 1.”
• Sheaves on affine Schubert varieties, modular representations and Lusztig's conjecture (2007, positive): “The following statement can be deduced from the results in Chapter XI of [Kum02].”
• Final group topologies, Kac-Moody groups and Pontryagin duality (2006, methodology): “In [62], it is called the analytic topology (more precisely, the analytic topology on Kumar’s group G restricts to the Kac-Petersen topology on our group G(A) ⊆ G), to distinguish it from the Zariski topology.”
• Eigenvalue problem and a new product in cohomology of flag varieties (2004, background): “β . Then, from [ Ku2 , 1.3.22.3] and (3), χw = ρ − 2ρ L + w −1 ρ, (9)”