BLOCK DECOMPOSITION VIA THE GEOMETRIC SATAKE EQUIVALENCE

Emilien Zabeth (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

We give a new proof for the description of the blocks in the category of representations of a reductive algebraic group G over a field of positive characteristic ℓ (originally due to Donkin), by working in the Satake category of the Langlands dual group and applying Smith-Treumann theory as developed by Riche and Williamson. On the representation theoretic side, our methods enable us to give a bound for the length of a minimum chain linking two weights in the same block, and to give a new proof for the block decomposition of a quantum group at an ℓ-th root of unity.

Domaines: Théorie des représentations [math.RT]

Emilien Zabeth. BLOCK DECOMPOSITION VIA THE GEOMETRIC SATAKE EQUIVALENCE. 2022. ⟨hal-03771461⟩