15 citations · 39 across the 12 of their papers we have counts for
14 papers
On Mirković-Vilonen polytopes
Pierre Baumann
Mirković-Vilonen polytopes encode in a geometrical way the numerical data present in the Kashiwara crystal of a semisimple group . We retrieve these polytopes from t…
Mirković-Vilonen basis in type A_1
Pierre Baumann, Arnaud Demarais
Let G be a reductive connected algebraic group over the field of complex numbers. Through the geometric Satake equivalence, the fundamental classes of the Mirković-Vilonen cycles d…
Bases of tensor products and geometric Satake correspondence
Pierre Baumann, Stéphane Gaussent, Peter Littelmann
The geometric Satake correspondence can be regarded as a geometric construction of the rational representations of a complex connected reductive group G. In their study of this cor…
The Mirkovic-Vilonen basis and Duistermaat-Heckman measures
Pierre Baumann, Joel Kamnitzer, Allen Knutson
Using the geometric Satake correspondence, the Mirkovic-Vilonen cycles in the affine Grasssmannian give bases for representations of a semisimple group G . We prove that these base…
Notes on the geometric Satake equivalence
Pierre Baumann, Simon Riche
These notes are devoted to a detailed exposition of the proof of the Geometric Satake Equivalence for general coefficients, following Mirkovic-Vilonen.
Chains in shard lattices and BHZ posets
Pierre Baumann, Frédéric Chapoton, Christophe Hohlweg +1
For every finite Coxeter group W , we prove that the number of chains in the shard intersection lattice introduced by Reading on the one hand and in the BHZ poset introduced by Ber…