Geodesic
On the double-affine Bruhat order: the ε=1 conjecture and classification of covers in ADE type
Muthiah, Dinakar1 ; Orr, Daniel2
1 Department of Mathematics and Statistics Lederle Graduate Research Tower 1623D University of Massachusetts Amherst 710 N. Pleasant Street Amherst MA 01003-9305 (USA)
2 Department of Mathematics MC 0123 460 McBryde Hall Virginia Tech 225 Stanger St. Blacksburg VA 24061 (USA)
Algebraic Combinatorics, Tome 2 (2019) no. 2, pp. 197-216.

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For any Kac–Moody group G, we prove that the Bruhat order on the semidirect product of the Weyl group and the Tits cone for G is strictly compatible with a ℤ-valued length function. We conjecture in general and prove for G of affine ADE type that the Bruhat order is graded by this length function. We also formulate and discuss conjectures relating the length function to intersections of “double-affine Schubert varieties”.

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DOI : 10.5802/alco.37
Classification : 05E10
Keywords: Kac–Moody groups, double-affine Bruhat order

Muthiah, Dinakar 1 ; Orr, Daniel 2

1 Department of Mathematics and Statistics Lederle Graduate Research Tower 1623D University of Massachusetts Amherst 710 N. Pleasant Street Amherst MA 01003-9305 (USA)
2 Department of Mathematics MC 0123 460 McBryde Hall Virginia Tech 225 Stanger St. Blacksburg VA 24061 (USA)
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {On the double-affine {Bruhat} order: the $\varepsilon =1$ conjecture and classification of covers in {ADE} type},
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     pages = {197--216},
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Muthiah, Dinakar; Orr, Daniel. On the double-affine Bruhat order: the $\varepsilon =1$ conjecture and classification of covers in ADE type. Algebraic Combinatorics, Tome 2 (2019) no. 2, pp. 197-216. doi : 10.5802/alco.37. http://geodesic.mathdoc.fr/articles/10.5802/alco.37/

[1] Björner, Anders; Brenti, Francesco Combinatorics of Coxeter groups, Graduate Texts in Mathematics, 231, Springer, 2005, xiv+363 pages | Zbl | MR

[2] Braverman, Alexander; Finkelberg, Michael Pursuing the double affine Grassmannian. I. Transversal slices via instantons on A k -singularities, Duke Math. J., Volume 152 (2010) no. 2, pp. 175-206 | Zbl | MR | DOI

[3] Braverman, Alexander; Kazhdan, David; Patnaik, Manish M. Iwahori-Hecke algebras for p-adic loop groups, Invent. Math., Volume 204 (2016) no. 2, pp. 347-442 | Zbl | MR | DOI

[4] Finkelberg, Michael; Mirković, Ivan Semi-infinite flags. I. Case of global curve ℙ 1 , Differential topology, infinite-dimensional Lie algebras, and applications (Advances in the Mathematical Sciences), Volume 194, American Mathematical Society, 1999, pp. 81-112 | Zbl | MR | DOI

[5] Kac, Victor G. Infinite-dimensional Lie algebras, Cambridge University Press, 1990, xxii+400 pages | Zbl | MR | DOI

[6] Muthiah, Dinakar On Iwahori-Hecke algebras for p-adic loop groups: double coset basis and Bruhat order, Am. J. Math., Volume 140 (2018) no. 1, pp. 221-244 | Zbl | MR | DOI

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