On the double-affine Bruhat order: the ε = 1 conjecture and classification of covers in ADE type

Muthiah, D. and Orr, D. (2019) On the double-affine Bruhat order: the ε = 1 conjecture and classification of covers in ADE type. Algebraic Combinatorics, 2(2), pp. 197-216. (doi: 10.5802/alco.37)

Abstract

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”.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Muthiah, Dr Dinakar
• Authors: Muthiah, D., and Orr, D.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Algebraic Combinatorics
• Publisher: MathOA
• ISSN: 2589-5486
• ISSN (Online): 2589-5486
• Published Online: 04 March 2019
• Copyright Holders: Copyright © The journal and the authors, 2019
• First Published: First published in Algebraic Combinatorics 2(2):197-216
• Publisher Policy: Reproduced under a Creative Commons license