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Cohomology for infinitesimal unipotent algebraic and quantum groups

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Abstract

In this paper we study the structure of cohomology spaces for the Frobenius kernels of unipotent and parabolic algebraic group schemes and of their quantum analogs. Given a simple algebraic group G, a parabolic subgroup P J , and its unipotent radical U J , we determine the ring structure of the cohomology ring H•((U J )1, k). We also obtain new results on computing H•((P J )1, L(λ)) as an L J -module where L(λ) is a simple G-module with highest weight λ in the closure of the bottom p-alcove. Finally, we provide generalizations of all our results to small quantum groups at a root of unity.

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Authors and Affiliations

  1. Department of Mathematics, University of Georgia, Athens, GA, 30602, USA

    Christopher M. Drupieski, Daniel K. Nakano & Nham V. Ngo

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  1. Christopher M. Drupieski
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  2. Daniel K. Nakano
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  3. Nham V. Ngo
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Correspondence to Christopher M. Drupieski.

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Supported in part by NSF VIGRE grant DMS-0738586.

Supported in part by NSF grant DMS-1002135.

Supported in part by NSF grant DMS-1002135.

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Drupieski, C.M., Nakano, D.K. & Ngo, N.V. Cohomology for infinitesimal unipotent algebraic and quantum groups. Transformation Groups 17, 393–416 (2012). https://doi.org/10.1007/s00031-012-9181-x

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