Robinson–Schensted–Knuth correspondence in the representation theory of the general linear group over a non-archimedean local field
2021 ◽
Vol 25
(22)
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pp. 644-678
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We construct new “standard modules” for the representations of general linear groups over a local non-archimedean field. The construction uses a modified Robinson–Schensted–Knuth correspondence for Zelevinsky’s multisegments. Typically, the new class categorifies the basis of Doubilet, Rota, and Stein (DRS) for matrix polynomial rings, indexed by bitableaux. Hence, our main result provides a link between the dual canonical basis (coming from quantum groups) and the DRS basis.
2005 ◽
Vol 92
(1)
◽
pp. 62-98
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1994 ◽
Vol 116
(1)
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pp. 7-25
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2009 ◽
Vol 80
(1)
◽
pp. 91-104
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1990 ◽
Vol 107
(2)
◽
pp. 193-196
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2018 ◽
Vol 85
(3-4)
◽
pp. 422
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