Ben Webster
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View article: BUBBLES IN THE AFFINE BRAUER AND KAUFFMAN CATEGORIES
BUBBLES IN THE AFFINE BRAUER AND KAUFFMAN CATEGORIES Open
We introduce a generating function approach to the affine Brauer and Kauffman categories, and show how it allows one to efficiently recover important sets of relations in these categories. We use this formalism to deduce restrictions on po…
View article: An update on Heisenberg and Kac-Moody categorification
An update on Heisenberg and Kac-Moody categorification Open
Heisenberg categories act on many Abelian categories appearing in type A representation theory. There is also a general procedure to construct from a Heisenberg action another action of a Kac-Moody 2-category for some associated Cartan mat…
View article: Steadied Khovanov-Lauda-Rouquier algebras and local models for blocks
Steadied Khovanov-Lauda-Rouquier algebras and local models for blocks Open
It's known that many different blocks of $\mathbb{F}_pS_n$ for different values of $n$ are equivalent as categories, though the corresponding block algebras are almost never isomorphic. Thus, it is a challenging problem to give one particu…
View article: Functoriality of Coulomb branches
Functoriality of Coulomb branches Open
We prove that the affine closure of the cotangent bundle of the parabolic base affine space for $\mathrm{GL}_n$ or $\mathrm{SL}_n$ is a Coulomb branch, which confirms a conjecture of Bourget-Dancer-Grimminger-Hanany-Zhong. In particular, w…
View article: Gelfand–Tsetlin modules in the Coulomb context
Gelfand–Tsetlin modules in the Coulomb context Open
This paper gives a new perspective on the theory of principal Galois orders, as developed by Futorny, Ovsienko, Hartwig, and others. Every principal Galois order can be written as for any idempotent in an algebra , which we call a flag G…
View article: Tilting Generator for the $T^*Gr(2,4)$ Coulomb Branch
Tilting Generator for the $T^*Gr(2,4)$ Coulomb Branch Open
Remarkable work of Kaledin, based on earlier joint work with Bezrukavnikov, has constructed a tilting generator of the category of coherent sheaves on a very general class of symplectic resolutions of singularities. In this paper, we give …
View article: Bubbles in the affine Brauer and Kauffman categories
Bubbles in the affine Brauer and Kauffman categories Open
We introduce a generating function approach to the affine Brauer and Kauffman categories and show how it allows one to efficiently recover important sets of relations in these categories. We use this formalism to deduce restrictions on pos…
View article: Degenerate twisted traces on quantized Kleinian singularities of type A
Degenerate twisted traces on quantized Kleinian singularities of type A Open
We study the space of non-degenerate traces on quantized Kleinian singularities of type A by studying their complement, the degenerate traces. In particular, we find the dimension of the space of twisted traces as a function of the corresp…
View article: RoCK blocks for affine categorical representations
RoCK blocks for affine categorical representations Open
Given a categorical action of a Lie algebra, a celebrated theorem of Chuang and Rouquier proves that the blocks corresponding to weight spaces in the same orbit of the Weyl group are derived equivalent, proving an even more celebrated conj…
View article: Voices from the field
Voices from the field Open
we (Oshish Ungras and Gavin Brockett, the editors of this iteration of Voices from the Field) invited higher education students, staff, and NGO representatives to join us for a conference on how we can create partnerships to address today'…
View article: Homological mirror symmetry for hypertoric varieties, I: Conic equivariant sheaves
Homological mirror symmetry for hypertoric varieties, I: Conic equivariant sheaves Open
We consider homological mirror symmetry in the context of hypertoric varieties, showing that appropriate categories of B-branes (that is, coherent sheaves) on an additive hypertoric variety match a category of A-branes on a Dolbeault hyper…
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: The nil-Brauer category
The nil-Brauer category Open
We introduce the nil-Brauer category and prove a basis theorem for its morphism spaces. This basis theorem is an essential ingredient required to prove that nil-Brauer categorifies the split -quantum group of rank one. As this -quantum gro…
View article: Twisted traces on abelian quantum Higgs and Coulomb branches
Twisted traces on abelian quantum Higgs and Coulomb branches Open
We study twisted traces on the quantum Higgs branches $A_{\operatorname{Higgs}}$ of $3d, \mathcal{N}=4$ gauge theories, that is, the quantum Hamiltonian reductions of Weyl algebras. In theories which are good, we define a twisted trace tha…
View article: 3-dimensional mirror symmetry
3-dimensional mirror symmetry Open
This expository article discusses recent advances in understanding 3-dimensional mirror symmetry and the mathematical definitions of the Higgs and Coulomb branches. This is a slightly expanded version of an article appearing in the Notices…
View article: On the representation theory of Schur algebras in type $B$
On the representation theory of Schur algebras in type $B$ Open
We study the representation theory of the type B Schur algebra $\mathcal{L}^n(m)$ with unequal parameters introduced in work of Lai, Nakano and Xiang. For generic values of $q,Q$, this algebra is semi-simple and Morita equivalent to the He…
View article: Nil-Brauer categorifies the split iquantum group of rank one
Nil-Brauer categorifies the split iquantum group of rank one Open
We prove that the Grothendieck ring of the monoidal category of finitely generated graded projective modules for the nil-Brauer category is isomorphic to an integral form of the split iquantum group of rank one. Under this isomorphism, the…
View article: The nil-Brauer category
The nil-Brauer category Open
We introduce the nil-Brauer category and prove a basis theorem for its morphism spaces. This basis theorem is an essential ingredient required to prove that nil-Brauer categorifies the split iquantum group of rank one. As this iquantum gro…
View article: RoCK blocks for affine categorical representations
RoCK blocks for affine categorical representations Open
Given a categorical action of a Lie algebra, a celebrated theorem of Chuang and Rouquier proves that the blocks corresponding to weight spaces in the same orbit of the Weyl group are derived equivalent, proving an even more celebrated conj…
View article: Coherent sheaves and quantum Coulomb branches II: quiver gauge theories and knot homology
Coherent sheaves and quantum Coulomb branches II: quiver gauge theories and knot homology Open
We continue our study of noncommutative resolutions of Coulomb branches in the case of quiver gauge theories. These include the Slodowy slices in type A and symmetric powers in $\mathbb{C}^2$ as special cases. These resolutions are based o…
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: Climate Action to transform Food Systems - Linking the UN Food Systems Summit and COP26 through initiatives that support greater resilience to climate change
Climate Action to transform Food Systems - Linking the UN Food Systems Summit and COP26 through initiatives that support greater resilience to climate change Open
The climate crisis is a major threat to our food systems, undermining decades of progress in providing more nutritious diets to a growing global population. Two key events take place in 2021 – the United Nations Food Systems Summit (UNFSS)…
View article: Gelfand-Tsetlin modules: canonicity and calculations
Gelfand-Tsetlin modules: canonicity and calculations Open
In this paper, we give a more down-to-earth introduction to the connection between Gelfand-Tsetlin modules over $\mathfrak{gl}_n$ and diagrammatic KLRW algebras, and develop some of its consequences. In addition to a new proof of this desc…
View article: On the definition of quantum Heisenberg category
On the definition of quantum Heisenberg category Open
We introduce a diagrammatic monoidal category [math] which we call the quantum Heisenberg category; here, [math] is “central charge” and [math] and [math] are invertible parameters. Special cases were known before: for central charge [math…