相关论文: On Cohen-Macaulayness of algebras generated by gen…
In this paper, we study properties of the algebras of planar quasi-invariants. These algebras are Cohen-Macaulay and Gorenstein in codimension one. Using the technique of matrix problems, we classify all Cohen-Macaulay modules of rank one…
The rings of quantum integrals of the generalized Calogero-Moser systems related to the deformed root systems ${\cal A}_n(m)$ and ${\cal C}_n(m,l)$ with integer multiplicities and corresponding algebras of quasi-invariants are investigated.…
The paper an elementary introduction for non-specialists to the theory of quasi-invariants of Coxeter groups. The main object of study is the variety X_m of quasi-invariants for a finite Coxeter group, which arose in a work of O.Chalykh and…
We use Macaulay's inverse system to study the Hilbert series for almost complete intersections generated by uniform powers of general linear forms. This allows us to give a classification of the Weak Lefschetz property for these algebras,…
Cohen-Macaulay Auslander algebras are the endomorphism algebras of representation generators of the subcategory of Gorenstein projective modules over $\rm{CM}$-finite algebras. In this paper, we study Cohen-Macaulay Auslander algebras over…
The deformed quantum Calogero-Moser-Sutherland problems related to the root systems of the contragredient Lie superalgebras are introduced. The construction is based on the notion of the generalized root systems suggested by V. Serganova.…
We define the cluster algebra associated with the Q-system for the Kirillov-Reshetikhin characters of the quantum affine algebra $U_q(\hat{\g})$ for any simple Lie algebra g, generalizing the simply-laced case treated in [Kedem 2007]. We…
We introduce quasi-invariant polynomials for an arbitrary finite complex reflection group W. Unlike in the Coxeter case, the space Q_k of quasi-invariants of a given multiplicity is not, in general, an algebra but a module over the…
Lewis, Reiner, and Stanton conjectured a Hilbert seriesfor a space of invariants under an action of finite general linear groups using $(q,t)$-binomial coefficients. This work gives an analog in positive characteristic of theorems relating…
In the past, empirical evidence has been presented that Hilbert series of symplectic quotients of unitary representations obey a certain universal system of infinitely many constraints. Formal series with this property have been called…
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…
In this paper, we shall prove that the integral subalgebra generated by the divided powers of the Drinfeld generators of an affine Kac-Moody algebra is an integral form. We compare this integral form with the analogous one derived from the…
We introduce and study deformations of finite-dimensional modules over rational Cherednik algebras. Our main tool is a generalization of usual harmonic polynomials for Coxeter groups -- the so-called quasiharmonic polynomials. A surprising…
Tilting theory is one of the central tools in modern representation theory, in particular in the study of Cohen-Macaulay representations. We study Cohen-Macaulay representations of $\mathbb N$-graded Artin-Schelter Gorenstein algebras $A$…
We obtain several results about representations of rational Cherednik algebras, and discuss their applications. Our first result is the Cohen-Macaulayness property (as modules over the polynomial ring) of Cherednik algebra modules with…
We study lowest-weight irreducible representations of rational Cherednik algebras attached to the complex reflection groups G(m,r,n) in characteristic p. Our approach is mostly from the perspective of commutative algebra. By studying the…
We investigate the Cohen-Macaulay property for rings of invariants under multiplicative actions of a finite group $G$. By definition, these are $G$-actions on Laurent polynomial algebras that stabilize the multiplicative group consisting of…
We study in detail the Jordan forms of the Coxeter transformations and prove shearing formulas due to Subbotin and Sumin for the characteristic polynomials of the Coxeter transformations. Using shearing formulas we calculate characteristic…
We give an overview of the representation theory of restricted rational Cherednik algebras. These are certain finite-dimensional quotients of rational Cherednik algebras at t=0. Their representation theory is connected to the geometry of…
The wave functions of quantum Calogero-Sutherland systems for trigonometric case are related to polynomials in l variables (l is a rank of root system) and they are the generalization of Gegenbauer polynomials and Jack polynomials. Using…