University of Denver

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19962026

most citedThe Large Area Telescope on the Fermi Gamma-ray Space Telescope Mission

4.1k citations

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20 papers · 1 filter

math.QA2024

On Virasoro-type reductions and inverse Hamiltonian reductions for $W$ -algebras and $W_{\infty}$ -algebras

Justine Fasquel, Vladimir Kovalchuk, Shigenori Nakatsuka

In this article, the Virasoro-type reduction and the corresponding inverse reductions are established for W-algebras associated with classical Lie type and nilpotent orbits of heig…

math.QA2022★ 2 cited

Orbifolds of Gaiotto-Rapčák $Y$ -algebras

Masoumah Al-Ali, Andrew R. Linshaw

The universal two-parameter $W_{\infty}$ -algebra is a classifying object for vertex algebras of type $W (2, 3, \dots, N)$ for some $N$ . Gaiotto and Rapčák recent…

math.QA2022★ 3 cited

Coloured $sl_{r}$ invariants of torus knots and characters of $W_{r}$ algebras

Shashank Kanade

Let $p < p^{'}$ be a pair of coprime positive integers. In this note, generalizing Morton's work in the case of $sl_{2}$ , we give a formula for the $sl_{r}$ Jones inva…

math.QA2022

Duality via convolution of W-algebras

Thomas Creutzig, Andrew R. Linshaw, Shigenori Nakatsuka +1

Feigin-Frenkel duality is the isomorphism between the principal $W$ -algebras of a simple Lie algebra $g$ and its Langlands dual Lie algebra $^{L} g$ .…

math.QA2021★ 11 cited

A note on odd reflections of super Yangian and Bethe ansatz

Kang Lu

In a recent paper arXiv:2109.09462, Molev introduced analogues of the odd reflections for the super Yangian $Y (gl_{m ∣ n})$ and obtained a transition rule for the…

math.QA2021★ 5 cited

Cosets of free field algebras via arc spaces

Andrew R. Linshaw, Bailin Song

Using the invariant theory of arc spaces, we find minimal strong generating sets for certain cosets of affine vertex algebras inside free field algebras that are related to classic…

math.QA2021★ 2 cited

Schur-Weyl duality for quantum toroidal superalgebras

Kang Lu

We establish the Schur-Weyl type duality between double affine Hecke algebras and quantum toroidal superalgebras, generalizing the well known result of Vasserot-Varagnolo [VV96] to…

math.QA2021★ 9 cited

Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra

Kang Lu

We give explicit actions of Drinfeld generators on Gelfand-Tsetlin bases of super Yangian modules associated with skew Young diagrams. In particular, we give another proof that the…

math.QA2020★ 8 cited

Generalized parafermions of orthogonal type

Thomas Creutzig, Vladimir Kovalchuk, Andrew R. Linshaw

There is an embedding of affine vertex algebras $V^{k} (gl_{n}) ↪ V^{k} (sl_{n + 1})$ , and the coset $\mathcal{C}^k(n) = \text{Com}(V^k(\mathfrak{gl}_n),…

math.QA2020★ 22 cited

Jacobi-Trudi identity and Drinfeld functor for super Yangian

Kang Lu, Evgeny Mukhin

We show that the quantum Berezinian which gives a generating function of the integrals of motions of XXX spin chains associated to super Yangian $Y (gl_{m ∣ n})$ c…

math.QA2019

Enumeration of racks and quandles up to isomorphism

Petr Vojtěchovský, Seung Yeop Yang

Racks and quandles are prominent set-theoretical solutions of the Yang-Baxter equation. We enumerate racks and quandles of orders $n \leq 13$ up to isomorphism, improving upon the pr…

math.QA2019★ 10 cited

On the supersymmetric XXX spin chains associated to $gl_{1∣1}$

Kang Lu, Evgeny Mukhin

We study the $gl_{1∣1}$ supersymmetric XXX spin chains. We give an explicit description of the algebra of Hamiltonians acting on any cyclic tensor products of polynomial…

math.QA2019★ 26 cited

Braided Tensor Categories related to $B_{p}$ Vertex Algebras

Jean Auger, Thomas Creutzig, Shashank Kanade +1

The $B_{p}$ -algebras are a family of vertex operator algebras parameterized by $p \in Z_{\geq 2}$ . They are important examples of logarithmic CFTs and appear as chir…

math.QA2019★ 31 cited

Gluing vertex algebras

Thomas Creutzig, Shashank Kanade, Robert McRae

We relate commutative algebras in braided tensor categories to braid-reversed tensor equivalences, motivated by vertex algebra representation theory. First, for $C$ a bra…

math.QA2018★ 24 cited

S-duality for the large $N = 4$ superconformal algebra

Thomas Creutzig, Davide Gaiotto, Andrew R. Linshaw

We prove some conjectures about vertex algebras which emerge in gauge theory constructions associated to the geometric Langlands program. In particular, we present the conjectural…

math.QA2018★ 94 cited

W-algebras as coset vertex algebras

Tomoyuki Arakawa, Thomas Creutzig, Andrew R. Linshaw

We prove the long-standing conjecture on the coset construction of the minimal series principal $W$ -algebras of $A D E$ types in full generality. We do this by first establishing Fei…

math.QA2016★ 86 cited

Schur-Weyl Duality for Heisenberg Cosets

Thomas Creutzig, Shashank Kanade, Andrew R. Linshaw +1

Let $V$ be a simple vertex operator algebra containing a rank $n$ Heisenberg vertex algebra $H$ and let $C = Com (H, V)$ be the coset of $H$ in $V$ . Assumin…

math.QA2015★ 65 cited

Simple current extensions beyond semi-simplicity

Thomas Creutzig, Shashank Kanade, Andrew R. Linshaw

Let V be a simple VOA and consider a representation category of V that is a vertex tensor category in the sense of Huang-Lepowsky. In particular, this category is a braided tensor…

math.QA2012★ 1 cited

A commutant realization of Odake's algebra

Thomas Creutzig, Andrew R. Linshaw

The bcβγ-system W of rank 3 has an action of the affine vertex algebra V_0(sl_2), and the commutant vertex algebra C =Com(V_0(sl_2), W) contains copies of V_{-3/2}(sl_2) and Odake'…

math.QA2012★ 25 cited

The super W_{1+\infty} algebra with integral central charge

Thomas Creutzig, Andrew R. Linshaw

The Lie superalgebra SD of regular differential operators on the super circle has a universal central extension \hat{SD}. For each c\in C, the vacuum module M_c(\hat{SD}) of centra…

On Virasoro-type reductions and inverse Hamiltonian reductions for W-algebras and W∞​-algebras

Orbifolds of Gaiotto-Rapčák Y-algebras

Coloured slr​ invariants of torus knots and characters of Wr​ algebras

Duality via convolution of W-algebras

A note on odd reflections of super Yangian and Bethe ansatz

Cosets of free field algebras via arc spaces

Schur-Weyl duality for quantum toroidal superalgebras

Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra

Generalized parafermions of orthogonal type

Jacobi-Trudi identity and Drinfeld functor for super Yangian

Enumeration of racks and quandles up to isomorphism

On the supersymmetric XXX spin chains associated to gl1∣1​

Braided Tensor Categories related to Bp​ Vertex Algebras

Gluing vertex algebras

S-duality for the large N=4 superconformal algebra

W-algebras as coset vertex algebras

Schur-Weyl Duality for Heisenberg Cosets

Simple current extensions beyond semi-simplicity

A commutant realization of Odake's algebra

The super W_{1+\infty} algebra with integral central charge

On Virasoro-type reductions and inverse Hamiltonian reductions for $W$ -algebras and $W_{\infty}$ -algebras

Orbifolds of Gaiotto-Rapčák $Y$ -algebras

Coloured $sl_{r}$ invariants of torus knots and characters of $W_{r}$ algebras

On the supersymmetric XXX spin chains associated to $gl_{1∣1}$

Braided Tensor Categories related to $B_{p}$ Vertex Algebras

S-duality for the large $N = 4$ superconformal algebra