15 citations · 39 across the 12 of their papers we have counts for
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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.
The canonical basis and the quantum Frobenius morphism
Pierre Baumann
The first goal of this paper is to study the amount of compatibility between two important constructions in the theory of quantized enveloping algebras, namely the canonical basis…