A homological interpretation of Jantzen's sum formula

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dc.creatorKulkarni, Upendra
dc.date2005-05-18
dc.date.accessioned2026-07-07T05:19:59Z
dc.date.available2026-07-07T05:19:59Z
dc.descriptionFor a split reductive algebraic group, this paper observes a homological interpretation for Weyl module multiplicities in Jantzen's sum formula. This interpretation involves an Euler characteristic built from Ext groups between integral Weyl modules. The new interpretation makes transparent For GL_n (and conceivable for other classical groups) a certain invariance of Jantzen's sum formula under "Howe duality" in the sense of Adamovich and Rybnikov. For GL_n a simple and explicit general formula is derived for the Euler characteristic between an arbitrary pair of integral Weyl modules. In light of Brenti's work on certain R-polynomials, this formula raises interesting questions about the possibility of relating Ext groups between Weyl modules to Kazhdan-Lusztig combinatorics.
dc.descriptionplain TeX, 22 pages
dc.identifierhttps://arxiv.org/abs/math/0505371
dc.identifierhttp://arxiv.org/abs/math/0505371
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75226
dc.subjectRepresentation Theory
dc.subject20G05; 20G10
dc.titleA homological interpretation of Jantzen's sum formula
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