arXiv subjects

Tim Cramer

Publications and source records attributed to Tim Cramer.

3 recordsLinked to original sources

arXiv2013

Kac's conjecture and the algebra of BPS states

Let Q be an affine quiver and let $\mathfrak{n}$ be the positive part of the affine Lie algebra associated to Q. We provide a construction of $\mathfrak{n}$ using the semistable irreducible components in the Lusztig nilpotent variety associated to Q. This confirms a conjecture of Frenkel, Malkin, and Vybornov on defining the so-called algebra of BPS states on the minimal resolution of a Kleinian singularity. Using the results of Crawley-Boevey and Van den Bergh, we show that our construction is closely connected to Kac's constant term conjecture in the case of an affine quiver.

math.RT↗

arXiv2009

Double Hall algebras and derived equivalences

We show that the reduced Drinfeld double of the Ringel-Hall algebra of a hereditary category is invariant under derived equivalences. By associating an explicit isomorphism to a given derived equivalence, we also extend the results of [BS1], [BS2], [SVdB], and [XY].

math.QA↗

arXiv2008

Heat Kernel Coefficients for Two-Dimensional Schrodinger Operators

In this note, we compute the Hadamard coefficients of (algebraically) integrable Schrodinger operators in two dimensions. These operators first appeared in [BL] and [B] in connection with Huygens' principle, and our result completes, in a sense, the investigation initiated in those papers.

math-ph↗