Related papers: Classification de modules aux diff\'erences filtr\…
We essentially achieve Birkhoff's program for q-difference equations by giving three different descriptions of the moduli space of isoformal analytic classes. This involves an extension of Birkhoff-Guenter normal forms, q-analogues of the…
The local analytic classification of irregular linear q-difference equations has recently been obtained by J.-P. Ramis, J. Sauloy and C. Zhang. Their description involves a q-analog of the Stokes sheaf and theorems of Malgrange-Sibuya type…
The local analytic classification and the description of the Galois group for complex linear analytic q-difference equations have been obtained by Ramis, Sauloy and Zhang [15, 14] under the assumption that the slopes of the Newton polygon…
We introduce and investigate new invariants on the pair of modules $M$ and $N$ over quantum affine algebras $U_q'(\mathfrak{g})$ by analyzing their associated R-matrices. From new invariants, we provide a criterion for a monoidal category…
We construct a 2-category of differential graded schemes. The local affine models in this theory are differential graded algebras, which are graded commutative with unit over a field of characteristic zero, are concentrated in non-positive…
We show that the Newton polygon of a linear q-difference equation depends only on the corresponding q-difference module. We interpret the classical results of convergent factorisation of Adams-Birkhoff-Guenther in terms of the existence of…
The simple integrable modules with finite dimensional weight spaces are classified for the quantum affine special linear superalgebra $\U_q(\hat{\mathfrak{sl}}(M|N))$ at generic $q$. Any such module is shown to be a highest weight or lowest…
In this note we first study regular $\mathbb{Z}$-graded local rings. We characterize commutative noetherian regular $\mathbb{Z}$-graded local rings in similar ways as in the usual local case. Then, we characterize graded isolated…
We give a definition for the restriction of a difference module on the affine line to a formal neighborhood of an orbit, trying to mimic the analogous definition and properties for a D-module. We show that this definition is reasonable in…
We classify irreducible finite-dimensional modules of a collection of real Lie superalgebras that includes the simple ones, their classical variants, complex Lie superalgebras after restriction of scalars, and all real Lie algebras. Our…
In persistent topology, q-tame modules appear as a natural and large class of persistence modules indexed over the real line for which a persistence diagram is definable. However, unlike persistence modules indexed over a totally ordered…
We define the categories of weight-finite modules over the type $\mathfrak a_1$ quantum affine algebra $\dot{\mathrm{U}}_q(\mathfrak a_1)$ and over the type $\mathfrak a_1$ double quantum affine algebra $\ddot{\mathrm{U}}_q(\mathfrak a_1)$…
We study the $qq$-character of quantum affine and toroidal algebra modules, with a focus on the role of spectral parameters. In particular, we revisit how their specialization affects the irreducibility of these modules.
This paper describes the classification of analytic $q$-difference equations. The difference Galois groups are computed. A tentative description of the universal difference Galois group is given.
In this paper, we explore a canonical connection between the algebra of $q$-difference operators $\widetilde{V}_{q}$, affine Lie algebra and affine vertex algebras associated to certain subalgebra $\mathcal{A}$ of the Lie algebra…
In this paper, we classify the finite dimensional irreducible modules for affine BMW algebra over an algebraically closed field with arbitrary characteristic.
Here is considered a specific detection loophole, that is relevant not only to testing of quantum nonlocality, but also to some other applications of quantum computations and communications. It is described by a simple affine relation…
We investigate the arithmetic of algebraic curves on coarse moduli spaces for special linear rank two local systems on surfaces with fixed boundary traces. We prove a structure theorem for morphisms from the affine line into the moduli…
Let $\Lambda$ be a basic finite dimensional algebra over an algebraically closed field, presented as a path algebra modulo relations; further, assume that $\Lambda$ is graded by lengths of paths. The paper addresses the classifiability, via…
We consider algebras defined over a complete, local and noetherian ground ring. They are gentle algebras in case the ground ring is a field. The unbounded homotopy category of complexes of projective modules is considered. Complexes with…