114 citations · 500 across the 43 of their papers we have counts for
27 papers · 1 filter
Category for truncated shifted Yangians and the bi-infinite Bott-Samelson variety
Joel Kamnitzer, Antoine Labelle, Alexis Leroux-Lapierre +2
In this paper, we study the category of representations of shifted Yangians associated to a simply-laced simple Lie algebra over . In parti…
Cactus flower spaces and monodromy of Bethe vectors
Joel Kamnitzer, Leonid Rybnikov
We continue the study of cactus flower moduli spaces and Gaudin models started in arXiv:2308.06880, arXiv:2407.06424. We show that isomorphism classes of operadic…
Fixed points of reverse Hessenberg convolution varieties
Joel Kamnitzer
Associated to any unit interval graph, Syu Kato introduced a variety which gives (via the geometric Satake correspondence) a graded representation whose character is the chr…
Gaudin models and moduli space of flower curves
Aleksei Ilin, Joel Kamnitzer, Leonid Rybnikov
We introduce and study the family of trigonometric Gaudin subalgebras in for arbitrary simple Lie algebra . This is the family of commutative subalgebras of ma…
Lie algebra actions on module categories for truncated shifted Yangians
Joel Kamnitzer, Ben Webster, Alex Weekes +1
We develop a theory of parabolic induction and restriction functors relating modules over Coulomb branch algebras, in the sense of Braverman-Finkelberg-Nakajima. Our functors gener…
Symplectic resolutions, symplectic duality, and Coulomb branches
Joel Kamnitzer
Symplectic resolutions are an exciting new frontier of research in representation theory. One of the most fascinating aspects of this study is symplectic duality: the observation t…
Heaps, crystals, and preprojective algebra modules
Anne Dranowski, Balazs Elek, Joel Kamnitzer +1
Fix a simply-laced semisimple Lie algebra. We study the crystal , were is a dominant minuscule weight and is a natural number. On one hand, can be realized…
Perfect bases in representation theory: three mountains and their springs
Joel Kamnitzer
In order to give a combinatorial descriptions of tensor product multiplicites for semisimple groups, it is useful to find bases for representations which are compatible with the ac…
Computing fusion products of MV cycles using the Mirkovic-Vybornov isomorphism
Roger Bai, Anne Dranowski, Joel Kamnitzer
The fusion of two Mirkovic-Vilonen cycles is a degeneration of their product, defined using the Beilinson-Drinfeld Grassmannian. In this paper, we put in place a conceptually eleme…
Hamiltonian reduction for affine Grassmannian slices and truncated shifted Yangians
Joel Kamnitzer, Khoa Pham, Alex Weekes
Generalized affine Grassmannian slices provide geometric realizations for weight spaces of representations of semisimple Lie algebras. They are also Coulomb branches, symplectic du…
BFN Springer Theory
Justin Hilburn, Joel Kamnitzer, Alex Weekes
Given a representation N of a reductive group G, Braverman-Finkelberg-Nakajima have defined a remarkable Poisson variety called the Coulomb branch. Their construction of this space…
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…
On category for affine Grassmannian slices and categorified tensor products
Joel Kamnitzer, Peter Tingley, Ben Webster +2
Truncated shifted Yangians are a family of algebras which naturally quantize slices in the affine Grassmannian. These algebras depend on a choice of two weights and for a L…
Crystals and monodromy of Bethe vectors
Iva Halacheva, Joel Kamnitzer, Leonid Rybnikov +1
Fix a semisimple Lie algebra g. Gaudin algebras are commutative algebras acting on tensor product multiplicity spaces for g-representations. These algebras depend on a parameter wh…
Reducedness of affine Grassmannian slices in type A
Joel Kamnitzer, Dinakar Muthiah, Alex Weekes +1
We prove in type A a conjecture which describes the ideal of transversal slices to spherical Schubert varieties in the affine Grassmannian. As a corollary, we prove a modular descr…
Comultiplication for shifted Yangians and quantum open Toda lattice
Michael Finkelberg, Joel Kamnitzer, Khoa Pham +2
We study a coproduct in type A quantum open Toda lattice in terms of a coproduct in the shifted Yangian of sl_2. At the classical level this corresponds to the multiplication of sc…
On a reducedness conjecture for spherical Schubert varieties and slices in the affine Grassmannian
Joel Kamnitzer, Dinakar Muthiah, Alex Weekes
We study spherical Schubert varieties in the affine Grassmannian. These Schubert varieties have a natural conjectural modular description due to Finkelberg-Mirković. This modular d…
Highest weights for truncated shifted Yangians and product monomial crystals
Joel Kamnitzer, Peter Tingley, Ben Webster +2
Truncated shifted Yangians are a family of algebras which are natural quantizations of slices in the affine Grassmannian. We study the highest weight representations of these algeb…
Quantum K-theoretic geometric Satake
Sabin Cautis, Joel Kamnitzer
The geometric Satake correspondence gives an equivalence of categories between the representations of a semisimple group and the spherical perverse sheaves on the affine Gras…
A combinatorial geometric Satake equivalence
Joel Kamnitzer
The geometric Satake correspondence provides an equivalence of categories between the Satake category of spherical perverse sheaves on the affine Grassmannian and the category of r…
Cyclic sieving, rotation, and geometric representation theory
Bruce Fontaine, Joel Kamnitzer
We study rotation of invariant vectors in tensor products of minuscule representations. We define a combinatorial notion of rotation of minuscule Littelmann paths. Using affine Gra…
Réflexions dans un cristal
Pierre Baumann, Stéphane Gaussent, Joel Kamnitzer
Let g = n^- + h + n^+ be a symmetrizable Kac-Moody algebra. Let B(\infty) be the Kashiwara crystal of U_q(n^-), let λbe a dominant integral weight, let T_λ= {t_λ} be the crystal wi…
Webs and quantum skew Howe duality
Sabin Cautis, Joel Kamnitzer, Scott Morrison
We give a diagrammatic presentation in terms of generators mod relations of the representation category of . More precisely, we produce all the relations amon…
Affine Mirković-Vilonen polytopes
Pierre Baumann, Joel Kamnitzer, Peter Tingley
Each integrable lowest weight representation of a symmetrizable Kac-Moody Lie algebra g has a crystal in the sense of Kashiwara, which describes its combinatorial properties. For a…