Related papers: Whittaker vectors for $\mathcal{W}$-algebras from …

We consider families of reductive complexes related by level-raising operators and originating from an associative algebra. In the main theorem it is shown that the multiple cohomology of that complexes is given by the factor space of…

We give a fully explicit description of Lie algebra derivatives (generalizing raising and lowering operators) for representations of SL(3,R) in terms of a basis of Wigner functions. This basis is natural from the point of view of principal…

In this paper we provide descriptions of the Whitehead groups with coefficients in a ring of the Hilbert modular group and its reduced version, as well as for the topological K-theory of $C^*$-algebras, after tensoring with $\mathbb{Q}$, by…

Following a general method proposed earlier, we construct here Wigner functions defined on coadjoint orbits of a class of semidirect product groups. The groups in question are such that their unitary duals consist purely of representations…

We consider moduli spaces of plane quartics marked with various structures such as Cayley octads, Aronhold heptads, Steiner complexes and G\"opel subsets and determine their cohomology. This answers a series of questions of Jesse Wolfson.…

We prove that the topological recursion formalism can be used to compute the WKB expansion of solutions of second order differential operators obtained by quantization of any hyper-elliptic curve. We express this quantum curve in terms of…

We compute the cohomology of modules over the algebra of twisted chiral differential operators over the flag manifold. This is applied to (1) finding the character of $G$-integrable irreducible highest weight modules over the affine Lie…

After recalling the construction of a graded Lie bracket on the space of cyclic multilinear forms on a vector space V, due to Georges Pinczon and Rosane Ushirobira, we prove this construction gives a structure of quadratic associative…

We introduce a new functor on categories of modular representations of reductive algebraic groups. Our functor has remarkable properties. For example it is a tensor functor and sends every standard and costandard object in the principal…

In this paper we provide an explicit construction of a $distinctive$ multiple Dirichlet series associated to products of quadratic Dirichlet L-series, which we believe should be tightly connected to a generalized metaplectic Whittaker…

We classify all groups G and all pairs (V,W) of absolutely simple Yetter-Drinfeld modules over G such that the support of the direct sum of V and W generates G, the square of the braiding between V and W is not the identity, and the Nichols…

We define twisted Hochschild homology for Green functors. This construction is the algebraic analogue of the relative topological Hochschild homology $THH_{C_n}(-)$, and it describes the $E_2$ term of the K\"unneth spectral sequence for…

In Part 1 of this paper, we study gravitational descendents of Gromov-Witten invariants for general projective manifolds, applying the Behrend-Fantechi construction of the virtual fundamental classes. In Part 2, we calculate the topological…

We describe the general strategy for lifting the Wess-Zumino-Witten model from the level of one-loop Kac-Moody $U_q(\widehat{\mathfrak{g}})_k$ to generic quantum toroidal algebras. A nearly exhaustive presentation is given for the two…

For a basic classical Lie superalgebra $\mathfrak s$, let $\mathfrak g$ be the central extension of the Takiff superalgebra $\mathfrak s\otimes\Lambda(\theta)$, where $\theta$ is an odd indeterminate. We study the category of $\mathfrak…

We develop a description of higher gauge theory with higher groupoids as gauge structure from first principles. This approach captures ordinary gauge theories and gauged sigma models as well as their categorifications on a very general…

In this paper, we study non-weight modules over gap-$p$ Virasoro algebras, including Whittaker modules, $\mathcal{U}(\mathbb{C} L_0)$-free modules and their tensor products. We establish necessary and sufficient conditions for universal…

We develop a theory of Goodwillie calculus for functors between $G$-equivariant homotopy theories, where $G$ is a finite group. We construct $J$-excisive approximations of a homotopy functor for any finite $G$-set $J$. These fit together…

We provide a description of the Drinfeld-Sokolov Hamiltonian reduction for the construction of classical W-algebras within the framework of Poisson vertex algebras. In this context, the gauge group action on the phase space is translated in…

We give a formula for a birational map on the Schubert cell associated to each Weyl group element of $G=\text{GL}(n)$. The map simplifies the UDL decomposition of matrices, providing structural insight into the Schubert cell decomposition…