On the center of quiver-Hecke algebras

We compute the equivariant cohomology ring of the moduli space of framed instantons over the affine plane. It is a Rees algebra associated with the center of cyclotomic degenerate affine Hecke algebras of type A. We also give some related results on the center of quiver Hecke algebras and cohomology of quiver varieties.Comment: 72 page

The decomposition of level-1 irreducible highest weight modules with respect to the level-0 actions of the quantum affine algebra Uq′(sl^n)U'_q(\hat{sl}_n)

We decompose the level-1 irreducible highest weight modules of the quantum affine algebra $U_q(\hat{sl}_n)$ with respect to the level-0 $U'_q (\hat{sl}_n)$--action defined in q-alg/9702024. The decomposition is parameterized by the skew Young diagrams of the border strip type.Comment: 22 pages, AMSLaTe

Appeal No. 0888: Edco Drilling and Producing, v. Division of Oil & Gas Resources Management

Chief\u27s Order 2014-254 (Hedrick #1A Well

Categorification of Highest Weight Modules via Khovanov-Lauda-Rouquier Algebras

In this paper, we prove Khovanov-Lauda's cyclotomic categorification conjecture for all symmetrizable Kac-Moody algebras. Let $U_q(g)$ be the quantum group associated with a symmetrizable Cartan datum and let $V(\Lambda)$ be the irreducible highest weight $U_q(g)$-module with a dominant integral highest weight $\Lambda$. We prove that the cyclotomic Khovanov-Lauda-Rouquier algebra $R^{\Lambda}$ gives a categorification of $V(\Lambda)$.Comment: Typoes correcte

Towards an open database of assessment material for STEM subjects: requirements and recommendations from early field trials

If appropriately implemented, open databases of instruction material may help teaching and learning by providing content for teaching activities, scaffolding, and self-assessment. The paper presents the current results of the development and implementation of a database that is expressly built for promoting exchange of questions and exercises, together with the associated solutions among teachers for STEM subjects. Besides presenting and motivating the initiative (together with reporting its current status), the manuscript lists a series of lessons that have been learned while executing the project - including the need for proper management of authorship and version control of the uploaded material. Moreover, the manuscript describes which features any open database of instruction material should implement to aid improved usability, together with a series of nontrivial theoretical and practical problems for future scientific investigations (e.g., developing taxonomies for indexing the difficulty levels of the instruction material uploaded in the database that do not suffer from the subjective interpretability associated with the existing taxonomies)

Some combinatorial identities related to commuting varieties and Hilbert schemes

In this article we explore some of the combinatorial consequences of recent results relating the isospectral commuting variety and the Hilbert scheme of points in the plane