Stratified Langlands duality in the An tower
Stratified Langlands duality in the An tower
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 nk //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.
math.KT, math.RT
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Wright, Nick
9f2fa5fe-f986-4672-a03b-ffb279e1760d
16 November 2016
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Wright, Nick
9f2fa5fe-f986-4672-a03b-ffb279e1760d
Niblo, Graham A., Plymen, Roger and Wright, Nick
(2016)
Stratified Langlands duality in the An tower
(MIMS EPrint, 2016.54)
University of Manchester
27pp.
Record type:
Monograph
(Working Paper)
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 nk //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.
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Accepted/In Press date: 1 April 2016
Published date: 16 November 2016
Additional Information:
27 pages
Keywords:
math.KT, math.RT
Organisations:
Mathematical Sciences, Pure Mathematics
Identifiers
Local EPrints ID: 407697
URI: http://eprints.soton.ac.uk/id/eprint/407697
PURE UUID: c69c5c6d-973a-4ed3-84ab-2c3effe821f0
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Date deposited: 22 Apr 2017 01:08
Last modified: 16 Mar 2024 02:44
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Contributors
Author:
Nick Wright
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