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SHEAVES ON THE ALCOVES AND MODULAR REPRESENTATIONS I

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Abstract

We consider the set of affine alcoves associated with a root system R as a topological space and define a certain category S of sheaves of \( {\mathcal{Z}}_k \)-modules on this space. Here \( {\mathcal{Z}}_k \) is the structure algebra of the root system over a field k. To any wall reection s we associate a wall crossing functor on S. In the companion article [FL] we prove that S encodes the simple rational characters of the connected, semisimple and simply connected algebraic group with root system R over k, in the case that k is algebraically closed with characteristic above the Coxeter number.

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Authors and Affiliations

  1. Department Mathematik, FAU Erlangen–Nürnberg, Cauerstraße 11, 91058, Erlangen, Germany

    P. FIEBIG

  2. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, I-00133, Rome, Italy

    M. LANINI

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  1. P. FIEBIG
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  2. M. LANINI
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Correspondence to M. LANINI.

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FIEBIG, P., LANINI, M. SHEAVES ON THE ALCOVES AND MODULAR REPRESENTATIONS I. Transformation Groups 25, 725–753 (2020). https://doi.org/10.1007/s00031-020-09563-7

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