Singular localization for Quantum groups at generic qq

We quantize parabolic flag manifolds and describe categories of equivariant quantum \D-modules on them at a singular central character. We compute global sections at any q \in \C^* and we also prove a singular version of Beilinson-Bernstein localization for a quantized enveloping algebra \Uq(\g), when $q$ is generic.Comment: 21 page

Higher Auslander-Reiten sequences and tt-structures

Let $R$ be an artin algebra and $\mathcal{C}$ an additive subcategory of $\operatorname{mod}(R)$. We construct a $t$-structure on the homotopy category $\operatorname{K}^{-}(\mathcal{C})$ whose heart $\mathcal{H}_{\mathcal{C}}$ is a natural domain for higher Auslander-Reiten (AR) theory. The abelian categories $\mathcal{H}_{\operatorname{mod}(R)}$ (which is the natural domain for classical AR theory) and $\mathcal{H}_{\mathcal{C}}$ interact via various functors. If $\mathcal{C}$ is functorially finite then $\mathcal{H}_{\mathcal{C}}$ is a quotient category of $\mathcal{H}_{\operatorname{mod}(R)}$. We illustrate the theory with two examples: Iyama developed a higher AR theory when $\mathcal{C}$ is a maximal $n$-orthogonal subcategory, see \cite{I}. In this case we show that the simple objects of $\mathcal{H}_{\mathcal{C}}$ correspond to Iyama's higher AR sequences and derive his higher AR duality from the existence of a Serre functor on the derived category $\operatorname{D}^b(\mathcal{H}_{\mathcal{C}})$. The category $\mathcal{O}$ of a complex semi-simple Lie algebra $\mathfrak{g}$ fits into higher AR theory by considering $R$ to be the coinvariant algebra of the Weyl group of $\mathfrak{g}$.Comment: 26 pages, accepted for publication in Journal of Algebra 201

Hochschild cohomology and string topology of global quotient orbifolds

Let M be a connected, simply connected, closed and oriented manifold, and G a finite group acting on M by orientation preserving diffeomorphisms. In this paper we show an explicit ring isomorphism between the orbifold string topology of the orbifold [M/G] and the Hochschild cohomology of the dg-ring obtained by performing the smash product between the group G and the singular cochain complex of M.Comment: Revised version. Sections have been reorganized, and section 4.1 is new. Version accepted for publication in the Journal of Topolog

Endomorphisms of quantized Weyl algebras

Belov-Kanel and Kontsevich conjectured that the group of automorphisms of the n'th Weyl algebra and the group of polynomial symplectomorphisms of C^2 are canonically isomorphic. We discuss how this conjecture can be approached by means of (second) quantized Weyl algebras at roots of unity

Röster från täckta ansikten

This study is based on the debate in Sweden over the past two years about a possible ban on face veils in schools, workplaces and public spaces. The aim of this paper is to shed light on one perspective that is often overlooked in this debate: that of the women who actually wear the face veil. Our study is based on conversational interviews with five women who are currently wearing, or have been wearing, face veils. We have also studied the debate in the Swedish national press and summarized their arguments for and against a ban on face veiling. For the purposes of this paper three overarching themes were investigated: Firstly we investigated the theological and internal Islamic debate on face veiling. Secondly, we focused on the debate surrounding a possible ban in the Swedish media. Our third focus is the women we have interviewed, and how their views relate to those expressed in the previous two realms. The primary questions to be answered in this study are: - How do the women we have interviewed motivate their wearing of the face veil? - What arguments were put forward in the debate on a possible ban on face veils in Swedish national press during the periods: 2009-09-20 ­ 2009-10-31 and 2010-08-01 ­ 2010-08-31? (These dates correspond with statements by various politicians favoring a ban, and with a report made to the Discrimination Ombudsman by a woman who wear the face veil. Two events that made the debate about a possible ban particularly topical.) - How do the women we have interviewed relate to the arguments put forward in the debate on the possible ban on face veils in Swedish national press? The five women we have interviewed were all born and raised in Sweden, and four out of five converted to Islam in their late teens or early twenties. We have found in this study that the women have various different motivations for their wearing of the face veil. Their interpretations and readings of the sources in Islam (The Quran and sunna) support their view that the face veil is a desirable practise within Islam. The women also points to the wearing of the face veil as enhancing their relationship with God. As previous research has shown, the veil is an important part in constructing a new religious identity as a Muslim woman. But the face veil cannot be reduced to a mere statement of a new religious identity; the spiritual reasons are a significant part of why these women wear the face veil. All the women stress the fact that they have made the decision to wear the face veil of their own free will, some to the vexation of their families. The women we have interviewed find the arguments favouring a ban (such as difficulties of communication, the face veil as a sign of gender inequalities and extremism etc.) to be superficial and often without grounds. The pro-ban arguments put forward in the debate voice concerns that the women themselves do not relate to. It seems clear that the debate attributes more meaning and symbolism to the veil and the women who wear it, than it can possibly contain, and the women relate to, such as Islamic extremism, the threat of the "other", anti democratic values etc

The cone of Betti diagrams over a hypersurface ring of low embedding dimension

We give a complete description of the cone of Betti diagrams over a standard graded hypersurface ring of the form k[x,y]/, where q is a homogeneous quadric. We also provide a finite algorithm for decomposing Betti diagrams, including diagrams of infinite projective dimension, into pure diagrams. Boij--Soederberg theory completely describes the cone of Betti diagrams over a standard graded polynomial ring; our result provides the first example of another graded ring for which the cone of Betti diagrams is entirely understood.Comment: Minor edits, references update

Galois cohomology of a number field is Koszul

We prove that the Milnor ring of any (one-dimensional) local or global field K modulo a prime number l is a Koszul algebra over Z/l. Under mild assumptions that are only needed in the case l=2, we also prove various module Koszulity properties of this algebra. This provides evidence in support of Koszulity conjectures that were proposed in our previous papers. The proofs are based on the Class Field Theory and computations with quadratic commutative Groebner bases (commutative PBW-bases).Comment: LaTeX 2e, 25 pages; v.2: minor grammatic changes; v.3: classical references added, remark inserted in subsection 1.6, details of arguments added in subsections 1.4, 1.7 and sections 5 and 6; v.4: still more misprints corrected, acknowledgement updated, a sentence inserted in section 4, a reference added -- this is intended as the final versio