Oded Yacobi
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View article: Normalisers of parabolic subgroups of Artin--Tits groups and Tits cone intersections
Normalisers of parabolic subgroups of Artin--Tits groups and Tits cone intersections Open
Let $Γ$ be a Coxeter diagram and let $J \subseteq Γ$. Motivated by 3-fold flops, Iyama and Wemyss study the hyperplane arrangement in the Tits cone intersection of $J$, which is a $J$-relative generalisation of the classical Coxeter arrang…
View article: Periodic Elements in Finite-Type Artin–Tits Groups and Stability Conditions
Periodic Elements in Finite-Type Artin–Tits Groups and Stability Conditions Open
Periodic elements in finite-type Artin–Tits groups are elements some positive power of which is central. We give a dynamical characterisation of periodic elements via their action on the corresponding 2-Calabi–Yau category and on its space…
View article: On the action of the Weyl group on canonical bases
On the action of the Weyl group on canonical bases Open
We study representations of simply-laced Weyl groups which are equipped with canonical bases. Our main result is that for a large class of representations, the separable elements of the Weyl group W act on these canonical bases by bijectio…
View article: 4-strand Burau is unfaithful modulo 5
4-strand Burau is unfaithful modulo 5 Open
We introduce a new algorithm for finding kernel elements in the Burau representation. Our algorithm applies reservoir sampling to a statistic on matrices which is closely correlated with Garside length. Using this we exhibit an explicit ke…
View article: Relations between generalised Gelfand-Tsetlin and Kazhdan-Lusztig bases of $S_n$
Relations between generalised Gelfand-Tsetlin and Kazhdan-Lusztig bases of $S_n$ Open
We prove that the Kazhdan-Lusztig basis of Specht modules is upper triangular with respect to all generalized Gelfand-Tsetlin bases constructed from any multiplicity-free tower of standard parabolic subgroups.
View article: Lie algebra actions on module categories for truncated shifted yangians
Lie algebra actions on module categories for truncated shifted yangians Open
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 generalize Bezrukavnikov-Etingof’s induction and restriction fun…
View article: 4-Strand Burau is Unfaithful Modulo 5
4-Strand Burau is Unfaithful Modulo 5 Open
We introduce a new algorithm for finding kernel elements in the Burau representation. Our algorithm applies reservoir sampling to a statistic on matrices which is closely correlated with Garside length. Using this we exhibit an explicit ke…
View article: Categorical braid group actions and cactus groups
Categorical braid group actions and cactus groups Open
Let g be a semisimple simply-laced Lie algebra of finite type. Let C be an abelian categorical representation of the quantum group Uq(g) categorifying an integrable representation V. The Artin braid group B of g acts on Db(C) by Rickard co…
View article: On Schützenberger modules of the cactus group
On Schützenberger modules of the cactus group Open
The cactus group acts on the set of standard Young tableaux of a given shape by (partial) Schützenberger involutions. It is natural to extend this action to the corresponding Specht module by identifying standard Young tableaux with the Ka…
View article: On the action of the Weyl group on canonical bases
On the action of the Weyl group on canonical bases Open
We study representations of simply-laced Weyl groups which are equipped with canonical bases. Our main result is that for a large class of representations, the separable elements of the Weyl group $W$ act on these canonical bases by biject…
View article: Lie algebra actions on module categories for truncated shifted Yangians
Lie algebra actions on module categories for truncated shifted Yangians Open
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 generalize Bezrukavnikov-Etingof's induction and restriction fun…
View article: On the action of the long cycle on the Kazhdan-Lusztig basis
On the action of the long cycle on the Kazhdan-Lusztig basis Open
The complex irreducible representations of the symmetric group carry an important canonical basis called the Kazhdan-Lusztig basis. Although it is difficult to express how general permutations act on this basis, some distinguished permutat…
View article: On the action of the long cycle on the Kazhdan-Lusztig basis
On the action of the long cycle on the Kazhdan-Lusztig basis Open
The complex irreducible representations of the symmetric group carry an important canonical basis called the Kazhdan-Lusztig basis. Although it is difficult to express how general permutations act on this basis, some distinguished permutat…
View article: On Schützenberger modules of the cactus group
On Schützenberger modules of the cactus group Open
The cactus group acts on the set of standard Young tableau of a given shape by (partial) Schützenberger involutions. It is natural to extend this action to the corresponding Specht module by identifying standard Young tableau with the Kazh…
View article: Categorical braid group actions and cactus groups
Categorical braid group actions and cactus groups Open
Let $\mathfrak{g}$ be a semisimple simply-laced Lie algebra of finite type. Let $\mathcal{C}$ be an abelian categorical representation of the quantum group $U_q(\mathfrak{g})$ categorifying an integrable representation $V$. The Artin braid…
View article: On a conjecture of Pappas and Rapoport about the standard local model for GL_<sub> <i>d</i> </sub>
On a conjecture of Pappas and Rapoport about the standard local model for GL_<sub> <i>d</i> </sub> Open
In their study of local models of Shimura varieties for totally ramified extensions, Pappas and Rapoport posed a conjecture about the reducedness of a certain subscheme of n × n {n\times n} matrices. We give a positive answer to their …
View article: The Equations Defining Affine Grassmannians in Type A and a Conjecture of Kreiman, Lakshmibai, Magyar, and Weyman
The Equations Defining Affine Grassmannians in Type A and a Conjecture of Kreiman, Lakshmibai, Magyar, and Weyman Open
The affine Grassmannian of $SL_n$ admits an embedding into the Sato Grassmannian, which further admits a Plücker embedding into the projectivization of Fermion Fock space. Kreiman, Lakshmibai, Magyar, and Weyman describe the linear part of…
View article: Quantum polynomial functors
Quantum polynomial functors Open
We construct a category of quantum polynomial functors which deforms Friedlander and Suslin's category of strict polynomial functors. The main aim of this paper is to develop from first principles the basic structural properties of this ca…
View article: A quantum Mirković-Vybornov isomorphism
A quantum Mirković-Vybornov isomorphism Open
We present a quantization of an isomorphism of Mirković and Vybornov which relates the intersection of a Slodowy slice and a nilpotent orbit closure in to a slice between spherical Schubert varieties in the affine Grassmannian of (with w…
View article: On a conjecture of Pappas and Rapoport about the standard local model\n for $GL_d$
On a conjecture of Pappas and Rapoport about the standard local model\n for $GL_d$ Open
In their study of local models of Shimura varieties for totally ramified\nextensions, Pappas and Rapoport posed a conjecture about the reducedness of a\ncertain subscheme of $n \\times n$ matrices. We give a positive answer to their\nconje…
View article: On a conjecture of Pappas and Rapoport about the standard local model for $GL_d$
On a conjecture of Pappas and Rapoport about the standard local model for $GL_d$ Open
In their study of local models of Shimura varieties for totally ramified extensions, Pappas and Rapoport posed a conjecture about the reducedness of a certain subscheme of $n \times n$ matrices. We give a positive answer to their conjectur…
View article: Highest weights for truncated shifted Yangians and product monomial crystals
Highest weights for truncated shifted Yangians and product monomial crystals Open
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 algebras. In particular, we conjecture that the possible highest …
View article: On category $\mathcal{O}$ for affine Grassmannian slices and categorified tensor products
On category $\mathcal{O}$ for affine Grassmannian slices and categorified tensor products Open
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 $λ$ and $μ$ for a Lie algebra $\mathfrak{g}$, which we will assume is simply-l…
View article: An equivalence between truncations of categorified quantum groups and Heisenberg categories
An equivalence between truncations of categorified quantum groups and Heisenberg categories Open
We introduce a simple diagrammatic 2-category $\\mathscr{A}$ that categorifies\nthe image of the Fock space representation of the Heisenberg algebra and the\nbasic representation of $\\mathfrak{sl}_\\infty$. We show that $\\mathscr{A}$ is\…
View article: The equations defining affine Grassmannians in type A and a conjecture\n of Kreiman, Lakshmibai, Magyar, and Weyman
The equations defining affine Grassmannians in type A and a conjecture\n of Kreiman, Lakshmibai, Magyar, and Weyman Open
The affine Grassmannian of $SL_n$ admits an embedding into the Sato\nGrassmannian, which further admits a Pl\\"ucker embedding into the\nprojectivization of Fermion Fock space. Kreiman, Lakshmibai, Magyar, and Weyman\ndescribe the linear p…
View article: Reducedness of affine Grassmannian slices in type A
Reducedness of affine Grassmannian slices in type A Open
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 description (due to Finkelberg-Mirković) of the spherical Schube…
View article: A quantum Mirković-Vybornov isomorphism
A quantum Mirković-Vybornov isomorphism Open
We present a quantization of an isomorphism of Mirković and Vybornov which relates the intersection of a Slodowy slice and a nilpotent orbit closure in $\mathfrak{gl}_N$ , to a slice between spherical Schubert varieties in the affine Grass…
View article: Highest weights for truncated shifted Yangians and product monomial\n crystals
Highest weights for truncated shifted Yangians and product monomial\n crystals Open
Truncated shifted Yangians are a family of algebras which are natural\nquantizations of slices in the affine Grassmannian. We study the highest weight\nrepresentations of these algebras. In particular, we conjecture that the\npossible high…
View article: Quantum Polynomial Functors
Quantum Polynomial Functors Open
We construct a category of quantum polynomial functors which deforms Friedlander and Suslin's category of strict polynomial functors. The main aim of this paper is to develop from first principles the basic structural properties of this ca…
View article: Quantum Polynomial Functors
Quantum Polynomial Functors Open
We construct a category of quantum polynomial functors which deforms Friedlander and Suslin's category of strict polynomial functors. The main aim of this paper is to develop from first principles the basic structural properties of this ca…