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Nilpotent cones and their representation theory

Publication ,  Journal Article
Brosnan, P; Pearlstein, G; Robles, C
January 31, 2016

We describe two approaches to classifying the possible monodromy cones C arising from nilpotent orbits in Hodge theory. The first is based upon the observation that C is contained in the open orbit of any interior point N in C under an associated Levi subgroup determined by the limit mixed Hodge structure. The possible relations between the interior of C its faces are described in terms of signed Young diagrams. The second approach is to understand the Tannakian category of nilpotent orbits via a category D introduced by Deligne in a letter to Cattani and Kaplan. In analogy with Hodge theory, there is a functor from D to a subcategory of SL(2)-orbits. We prove that these fibers are, roughly speaking, algebraic. We also give a correction to a result of K. Kato.

Duke Scholars

Publication Date

January 31, 2016
 

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Brosnan, P., Pearlstein, G., & Robles, C. (2016). Nilpotent cones and their representation theory.
Brosnan, P., G. Pearlstein, and C. Robles. “Nilpotent cones and their representation theory,” January 31, 2016.
Brosnan P, Pearlstein G, Robles C. Nilpotent cones and their representation theory. 2016 Jan 31;
Brosnan, P., et al. Nilpotent cones and their representation theory. Jan. 2016.
Brosnan P, Pearlstein G, Robles C. Nilpotent cones and their representation theory. 2016 Jan 31;

Publication Date

January 31, 2016