We will follow the notations of [7]. Let (Y,X, . . . ) be a simply connected root datum of finite type. Let p be a prime number bigger than the Coxeter number h. Let ζ be a primitive p-th root of unity in C. Let U be the quantum group with divided powers associated to these data. Let T be the category of tilting modules over U , see e.g. [1]. Recall that any tilting module is a sum of indecompo...

Thirty-five teenage patients with a history of presyncope or syncope underwent a passive head-up tilting to reproduce symptoms of syncope. If tilting alone did not induce syncope, isoproterenol infusion was given to increase heart rate to 150 to 160 beats per minute. In 80% of patients with a history of syncope, identical symptoms could be reproduced during tilting: an abrupt fall in blood pres...

If (A,B) and (A′,B′) are co-t-structures of a triangulated category, then (A′,B′) is called intermediate if A ⊆ A′ ⊆ ΣA. Our main results show that intermediate co-t-structures are in bijection with two-term silting subcategories, and also with support τ -tilting subcategories under some assumptions. We also show that support τ -tilting subcategories are in bijection with certain finitely gener...

We show how to express the characters of tilting modules in a (possibly parabolic) category O over a Kac-Moody algebra in terms of the characters of simple highest weight modules. This settles, in lots of cases, Conjecture 7.2 of Kazhdan-Lusztig-Polynome and eine Kombinatorik für Kipp-Moduln, Representation Theory (An electronic Journal of the AMS) (1997), by the author, describing the characte...

We show that every tilting module of projective dimension one over a ring R is associated in a natural way to the universal localization R → RU at a set U of finitely presented modules of projective dimension one. We then investigate tilting modules of the form RU ⊕ RU/R. Furthermore, we discuss the relationship between universal localization and the localization R → QG given by a perfect Gabri...

We show how to express the characters of tilting modules in a (possibly parabolic) category O over a Kac-Moody algebra in terms of the characters of simple highest weight modules. This settles in lots of cases Conjecture 7.2 in Kazhdan-Lusztig-Polynome und eine Kombinatorik für KippModuln, Represent. Theory (1997), by the author, describing the character of tilting modules for quantum groups at...

Harnessing wind energy is one of the pressing challenges of our time. The scale, complexity, and robustness of wind power systems present compelling cyber-physical system design issues. In response to these emerging challenges, Purdue has initiated strategic partnerships for infrastructure development. Working with the US Department of Energy, Purdue is developing physical infrastructure for an...

We study perfect fluid cosmological models with a constant equation of state parameter γ in which there are two naturally defined time-like congruences, a geometrically defined geodesic congruence and a non-geodesic fluid congruence. We establish an appropriate set of boost formulae relating the physical variables, and consequently the observed quantities, in the two frames. We study expanding ...

We use Kazhdan-Lusztig tensoring to, first, describe annihilating ideals of highest weight modules over an affine Lie algebra in terms of the corresponding VOA and, second, to classify tilting functors, an affine analogue of projective functors known in the case of a simple Lie algebra.

The purpose of this chapter is to give an introduction to the theory of cluster categories and cluster-tilted algebras, with some background on the theory of cluster algebras, which motivated these topics. We will also discuss some of the interplay between cluster algebras on one side and cluster categories/cluster-tilted algebras on the other, as well as feedback from the latter theory to clus...