The Formal Affine Demazure Algebra and Real Finite Reflection Groups

@article{Gandhi2022TheFA,
  title={The Formal Affine Demazure Algebra and Real Finite Reflection Groups},
  author={Raja Rama Gandhi},
  journal={Algebras and Representation Theory},
  year={2022}
}
  • R. Gandhi
  • Published 17 May 2019
  • Mathematics
  • Algebras and Representation Theory
. In this paper, we generalize the formal affine Demazure algebra of Hoffnung-Malag´on-L´opez- Savage-Zainoulline to all real finite reflection groups. We begin by generalizing the formal group ring of Calm`es-Petrov-Zainoulline to all real finite reflection groups. We then define and study the formal Demazure operators that act on the formal group ring. Using these results and constructions, we define and study the formal affine Demazure algebra for all real finite reflection groups. Finally, we compute… 

References

SHOWING 1-10 OF 27 REFERENCES

Invariants, torsion indices and oriented cohomology of complete flags

In the present notes we generalize the classical work of Demazure [Invariants sym\'etriques entiers des groupes de Weyl et torsion] to arbitrary oriented cohomology theories and formal group laws.

Formal Hecke algebras and algebraic oriented cohomology theories

In the present paper, we generalize the construction of the nil Hecke ring of Kostant–Kumar to the context of an arbitrary formal group law, in particular, to an arbitrary algebraic oriented

A coproduct structure on the formal affine Demazure algebra

In the present paper, we generalize the coproduct structure on nil Hecke rings introduced and studied by Kostant and Kumar to the context of an arbitrary algebraic oriented cohomology theory and its

Push-pull operators on the formal affine Demazure algebra and its dual

In the present paper we introduce and study the push pull operators on the formal affine Demazure algebra and its dual. As an application we provide a non-degenerate pairing on the dual of the formal

The nil Hecke ring and cohomology of G/P for a Kac-Moody group G.

TLDR
A ring R is constructed, which is very simply and explicitly defined as a functor of W together with the W-module [unk] alone and such that all these four structures on H(*)(G/B) arise naturally from the ring R.

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

On the integral basis of the maximal real subfield of a cyclotomic field.

Let C„ be a primitive n-th root of unity and #=(?(£,, + ζ') be the maximal real subfield of the n-th cyclotomic field Q(£n). It is proved in this paper that &»!_! {l, ς + C, . . ., (ί,, + Ο 2 } is an

The arithmetic of elliptic curves

  • J. Silverman
  • Mathematics, Computer Science
    Graduate texts in mathematics
  • 1986
TLDR
It is shown here how Elliptic Curves over Finite Fields, Local Fields, and Global Fields affect the geometry of the elliptic curves.

On the ring of integers of real cyclotomic fields

: Let (cid:2) n be a primitive n th root of unity. As is well known, Z ½ (cid:2) n þ (cid:2) (cid:3) 1 n (cid:4) is the ring of integers of Q ð (cid:2) n þ (cid:2) (cid:3) 1 n Þ . We give an

Désingularisation des variétés de Schubert généralisées

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