相关论文: The point variety of quantum polynomial rings
For a group $G$ acting on an affine variety $X$, the separating variety is the closed subvariety of $X\times X$ encoding which points of $X$ are separated by invariants. We concentrate on the indecomposable rational linear representations…
The multivariate quantum $q$-Krawtchouk polynomials are shown to arise as matrix elements of "$q$-rotations" acting on the state vectors of many $q$-oscillators. The focus is put on the two-variable case. The algebraic interpretation is…
We define a GL-variety to be a (typically infinite dimensional) algebraic variety equipped with an action of the infinite general linear group under which the coordinate ring forms a polynomial representation. Such varieties have been used…
The gauge invariant observables of the closed bosonic string are quantized without anomalies in four space-time dimensions by constructing their quantum algebra in a manifestly covariant approach. The quantum algebra is the kernel of a…
A way to construct and classify the three dimensional polynomially deformed algebras is given and the irreducible representations is presented. for the quadratic algebras 4 different algebras are obtained and for cubic algebras 12 different…
We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…
This paper defines the concept of an oriented quantum algebra and develops its application to the construction of quantum link invariants. We show that all known quantum link invariants can be put into this framework.
We study irreducible representations of a class of quantum spheres, quotients of quantum symplectic spheres.
The goals of this article are as follows: (1) To determine the irreducible components of the affine varieties parametrizing the representations of $ \Lambda $ with dimension vector d, where $ \Lambda $ traces a major class of finite…
Quantum deformations of sets of points of the real and the complexified projective line are constructed. These deformations depend on the deformation parameter q and certain further parameters \lambda_{ij}. The deformations for which the…
Answering a question of Frank Calegari, we extend some of our earlier results on dimension of fixed point spaces of elements in irreducible linear groups. We consider characteristic polynomials rather than just fixed spaces.
The $q$-binomial coefficients are q-analogues of the binomial coefficients, counting the number of $k$-dimensional subspaces in the $n$-dimensional vector space $\mathbb{F}^n_q$ over $\mathbb{F}_{q}$. In this paper, we define a Euclidean…
We give a coalgebra structure on 1-vertex irreducible graphs which is that of a cocommutative coassociative graded connected coalgebra. We generalize the coproduct to the algebraic representation of graphs so as to express a bare 1-particle…
In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…
We give a general method for proving quantum lower bounds for problems with small range. Namely, we show that, for any symmetric problem defined on functions $f:\{1, ..., N\}\to\{1, ..., M\}$, its polynomial degree is the same for all…
The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…
It is proved that each of compact linear groups of one special type admits a polynomial factorization map onto a real vector space. More exactly, the group is supposed to be non-commutative one-dimensional and to have two connected…
We investigate the properties of the inverse limit of the algebras of local unitary invariant polynomials of quantum systems containing various types of fermionic and/or bosonic particles as the dimensions of the single particle state…
We prove that certain quiver varieties are irreducible and therefore are isomorphic to Hilbert schemes of points of the total spaces of the bundles $\mathcal O_{\mathbb P^1}(-n)$ for $n \ge 1$.
We establish a quantum cluster algebra structure on the quantum Grothendieck ring of a certain monoidal subcategory of the category of finite-dimensional representations of a simply-laced quantum affine algebra. Moreover, the…