Related papers: Lower bound cluster algebras: presentations, Cohen…
We consider boundary scattering for a semi-infinite one-dimensional deformed Hubbard chain with boundary conditions of the same type as for the Y=0 giant graviton in the AdS/CFT correspondence. We show that the recently constructed quantum…
In this paper we completely classify all the special Cohen-Macaulay (=CM) modules corresponding to the exceptional curves in the dual graph of the minimal resolutions of all two dimensional quotient singularities. In every case we exhibit…
A universality of deformed Heisenberg algebra involving the reflection operator is revealed. It is shown that in addition to the well-known infinite-dimensional representations related to parabosons, the algebra has also finite-dimensional…
The higher-spin (HS) algebras so far known can be interpreted as the symmetries of the minimal representation of the isometry algebra. After discussing this connection briefly, we generalize this concept to any classical Lie algebras and…
By Auslander's algebraic McKay correspondence, the stable category of Cohen-Macaulay modules over a simple singularity is equivalent to the $1$-cluster category of the path algebra of a Dynkin quiver (i.e. the orbit category of the derived…
In this paper we show that the Cuntz--Pimsner algebras associated to minimal homeomorphisms twisted by line bundles, along with their orbit-breaking subalgebras, are $\mathcal{Z}$-stable whenever the underlying dynamical system has the…
We develop an analogue of the deformation to the normal cone in the context of derived algebraic geometry. This provides any given morphism of derived stacks with a degeneration to the zero section of its normal bundle (i.e., its 1-shifted…
We consider two algebras of curves associated to an oriented surface of finite type - the cluster algebra from combinatorial algebra, and the skein algebra from quantum topology. We focus on generalizations of cluster algebras and…
Recently Pascal Baseilhac and Stefan Kolb obtained a PBW basis for the $q$-Onsager algebra $\mathcal O_q$. They defined the PBW basis elements recursively, and it is obscure how to express them in closed form. To mitigate the difficulty, we…
We describe a ring whose category of Cohen-Macaulay modules provides an additive categorification of the cluster algebra structure on the homogeneous coordinate ring of the Grassmannian of k-planes in n-space. More precisely, there is a…
We give a combinatorial characterization of amenability of monomial algebras and prove the existence of monomial Folner sequences, answering a question due to Ceccherini-Silberstein and Samet-Vaillant. We then use our characterization to…
A finite projective plane, or more generally a finite linear space, has an associated incidence complex that gives rise to two natural algebras: the Stanley-Reisner ring $R/I_\Lambda$ and the inverse system algebra $R/I_\Delta$. We give a…
A large family of "standard" coboundary Hopf algebras is investigated. The existence of a universal R-matrix is demonstrated for the case when the parameters are in general position. Special values of the parameters are characterized by the…
In this paper, we study the Cohen-Macaulayness of non-affine normal semigroups in $\mathbb{Z}^n$. We do this by establishing the following four statements each of independent interest: 1) a Lazard type result on $I$-supported elements of…
We prove quantitative versions of Borel and Harish-Chandra's theorems on reduction theory for arithmetic groups. Firstly, we obtain polynomial bounds on the lengths of reduced integral vectors in any rational representation of a reductive…
We say that a set $S$ is $\Delta^0_{(n)}(X)$ if membership of $n$ in $S$ is a $\Delta^0_{n}(X)$ question, uniformly in $n$. A set $X$ is low for $\Delta$-Feiner if every set $S$ that is $\Delta^0_{(n)}(X)$ is also…
We investigate the representation theory of the rational and trigonometric Cherednik algebra of type $GL_n$ by means of combinatorics on periodic (or cylindrical) skew diagrams. We introduce and study standard tableaux and plane partitions…
Various mixing properties of $\beta$-, $\beta'$- and Gaussian Delaunay tessellations in $\mathbb{R}^{d-1}$ are studied. It is shown that these tessellation models are absolutely regular, or $\beta$-mixing. In the $\beta$- and the Gaussian…
Monomial ideals which are generic with respect to either their generators or irreducible components have minimal free resolutions derived from simplicial complexes. For a generic monomial ideal, the associated primes satisfy a saturated…
We establish a Poincar\'e-Dulac theorem for sequences (G_n)_n of holomorphic contractions whose differentials d_0 G_n split regularly. The resonant relations determining the normal forms hold on the moduli of the exponential rates of…