Stratified Langlands duality in the A_n tower

Niblo, Graham and Plymen, Roger and Wright, Nick (2016) Stratified Langlands duality in the A_n tower. [MIMS Preprint]

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Abstract

Let S_k denote a maximal torus in the complex Lie group G = SL_n(C)/C_k and let T_k denote a maximal torus in its compact real form SU_n(C)/C_k, where k divides n. Let W denote the Weyl group of G, namely the symmetric group S_n. We elucidate the structure of the extended quotient S_k // W as an algebraic variety and of T_k // W as a topological space, in both cases describing them as bundles over unions of tori. Corresponding to the invariance of K-theory under Langlands duality, this calculation provides a homotopy equivalence between T_k // W and its dual T_{n/k} // W. Hence there is an isomorphism in cohomology for the extended quotients which is stratified as a direct sum over conjugacy classes of the Weyl group. We use our formula to compute a number of examples.

Item Type: MIMS Preprint
Uncontrolled Keywords: Langlands duality, K-theory, Lie groups
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 19 K-theory
MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups
Depositing User: Professor Roger Plymen
Date Deposited: 18 Nov 2016
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2513

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