# 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} }

. 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

- Mathematics
- 2009

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

- MathematicsSelecta Mathematica
- 2013

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

- Mathematics
- 2016

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

- Mathematicsmanuscripta mathematica
- 2018

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.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1986

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

- Mathematics
- 1987

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.

- Mathematics
- 1976

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

- Mathematics, Computer ScienceGraduate texts in mathematics
- 1986

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

- Mathematics
- 2016

: 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

- Philosophy
- 1974

© Gauthier-Villars (Editions scientifiques et medicales Elsevier), 1974, tous droits reserves. L’acces aux archives de la revue « Annales scientifiques de l’E.N.S. » (http://www.…