Related papers: Quantization of the minimal nilpotent orbits and t…

Let $\mathfrak{g}$ be a finite simply-laced type simple Lie algebra. Baumann-Kamnitzer-Knutson recently defined an algebra morphism $\overline{D}$ on the coordinate ring $\mathbb{C}[N]$ related to Brion's equivariant multiplicities via the…

We prove an equidistribution result about Hecke orbits on the Picard group of Shimura curves coming from definite quaternion algebras over function fields. In particular, we show the equidistribution of Hecke orbits of supersingular…

We study extremal black hole solutions of the S3 model (obtained by setting S=T=U in the STU model) using group theoretical methods. Upon dimensional reduction over time, the S3 model exhibits the pseudo-Riemannian coset structure G/K with…

We consider the Lie algebra $\mathfrak{g}$ of a simple, simply connected algebraic group over a field of large positive characteristic. For each nilpotent orbit $\mathcal{O} \subseteq \mathfrak{g}$ we choose a representative $e\in…

We construct natural extensions of the Kudla--Millson generating series of cohomology classes of special cycles in compactified unitary Shimura varieties of signature $(n+1,1)$ and prove that they are holomorphic Hermitian modular forms.…

The Broadhurst-Kreimer (BK) conjecture describes the Hilbert series of a bigraded Lie algebra A related to the multizeta values. Brown proposed a conjectural description of the homology of this Lie algebra (homological conjecture (HC)), and…

For any finite dimensional algebra $\Lambda$ given by a quiver with relations, we prove that its dg singularity category is quasi-equivalent to the perfect dg derived category of a dg Leavitt path algebra. The result might be viewed as a…

For a finite quiver without sinks, we establish an isomorphism in the homotopy category $\mathrm {Ho}(B_\infty)$ of $B_{\infty}$-algebras between the Hochschild cochain complex of the Leavitt path algebra $L$ and the singular Hochschild…

Following the approach of Haiden-Katzarkov-Kontsevich arXiv:1409.8611, to any homologically smooth graded gentle algebra $A$ we associate a triple $(\Sigma_A, \Lambda_A; \eta_A)$, where $\Sigma_A$ is an oriented smooth surface with…

The present paper is devoted to study the effect of connected and disconnected rotations of G\"odel algebras with operators grounded on directly indecomposable structures. The structures resulting from this construction we will present are…

We show that Nichols algebras of most simple Yetter-Drinfeld modules over the projective special linear group over a finite field, corresponding to semisimple orbits, have infinite dimension. We introduce a new criterium to determine when a…

The Drinfeld double D of the bosonization of a finite-dimensional Nichols algebra B(V) over a finite non-abelian group G is called a quantum group at a non-abelian group. We introduce Verma modules over such a quantum group D and prove that…

Let $\FRAK{g}$ be a classical simple Lie superalgebra. To every nilpotent orbit $\cal O$ in $\FRAK{g}_0$ we associate a Clifford algebra over the field of rational functions on $\cal O$. We find the rank, $k(\cal O)$ of the bilinear form…

We present a new proof of a part of the nilpotent orbit theorem for unipotent complex variations of Hodge structure. In our proof, the $L^2$ extension theorem of Ohsawa-Takegoshi type plays an essential role.

The purpose of this paper is to prove that we can construct all finite dimensional irreducible nilpotent modules of type 1 inductively by using Schnizer homomorphisms for quantum algebra at roots of unity of type A, B, C, D or G.

We consider the socle deformations arising from formal deformations of a class of Koszul self-injective special biserial algebras which occur in the study of the Drinfeld double of the generalized Taft algebras. We show, for these…

We define a genuine $\mathbb{Z}/2$-equivariant real algebraic $K$-theory spectrum $KR(A)$, for every genuine $\mathbb{Z}/2$-equivariant spectrum $A$ equipped with a compatible multiplicative structure. This construction extends the real…

We develop a fundamental theory of compact quantum group equivariant finite extensions of C*-algebras. In particular we focus on the case of quantum homogeneous spaces and give a Tannaka-Krein type result for equivariant correspondences. As…

We study the local properties of a class of codimension-2 defects of the 6d N=(2,0) theories of type J=A,D,E labeled by nilpotent orbits of a Lie algebra \mathfrak{g}, where \mathfrak{g} is determined by J and the outer-automorphism twist…

Using the mirror theorem [CCIT15], we give a Landau-Ginzburg mirror description for the big equivariant quantum cohomology of toric Deligne-Mumford stacks. More precisely, we prove that the big equivariant quantum D-module of a toric…