Irreducible Modules over Finite Simple Lie Pseudoalgebras I. Primitive Pseudoalgebras of Type W and S

One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra [K]. A Lie pseudoalgebra is a generalization of the notion of a Lie conformal algebra for which C[\partial] is replaced by the universal enveloping algebra H of a finite-dimensional Lie algebra [BDK]. The finite (i.e., finitely generated over H) simple Lie pseudoalgebras were classified in [BDK]. In a series of papers, starting with the present one, we classify all irreducible finite modules over finite simple Lie pseudoalgebras.Comment: 51 pages; minor change

GAFA Geometric And Functional Analysis FINITE JET DETERMINATION OF LOCAL ANALYTIC CR AUTOMORPHISMS AND THEIR PARAMETRIZATION BY 2-JETS IN THE FINITE

We show that germs of local real-analytic CR automorphisms of a real-analytic hypersurface M in C 2 at a point p ∈ M are uniquely determined by their jets of some finite order at p if and only if M is not Levi-flat near p. This seems to be the first necessary and sufficient result on finite jet determination and the first result of this kind in the infinite type case. If M is of finite type at p, we prove a stronger assertion: the local real-analytic CR automorphisms of M fixing p are analytically parametrized (and hence uniquely determined) by their 2-jets at p. This result is optimal since the automorphisms of the unit sphere are not determined by their 1-jets at a point of the sphere. The finite type condition is necessary since otherwise the needed jet order can be arbitrarily high [Kow1,2], [Z2]. Moreover, we show, by an example, that determination by 2-jets fails for finite type hypersurfaces already in C3. We also give an application to the dynamics of germs of local biholomorphisms of C 2.

Tokuyama-type formulas for type B

We obtain explicit formulas for the product of a deformed Weyl denominator with the character of an irreducible representation of the spin group $\rm{Spin}_{2r+1}({\mathbb C})$, which is an analogue of the formulas of Tokuyama for Schur polynomials and Hamel-King for characters of symplectic groups. To give these, we start with a symplectic group and obtain such characters using the Casselman-Shalika formula. We then analyze this using objects which are naturally attached to the metaplectic double cover of an odd orthogonal group, which also has dual group $\rm{Spin}_{2r+1}({\mathbb C})$.Comment: 34 pages. To appear in Israel J. of Mat

Classification of GHZ-type, W-type and GHZ-W-type multiqubit entanglements

We propose the concept of SLOCC-equivalent basis (SEB) in the multiqubit space. In particular, two special SEBs, the GHZ-type and the W-type basis are introduced. They can make up a more general family of multiqubit states, the GHZ-W-type states, which is a useful kind of entanglement for quantum teleporatation and error correction. We completely characterize the property of this type of states, and mainly classify the GHZ-type states and the W-type states in a regular way, which is related to the enumerative combinatorics. Many concrete examples are given to exhibit how our method is used for the classification of these entangled states.Comment: 16 pages, Revte

Comparing the Host Galaxies of Type Ia, Type II and Type Ibc Supernovae

We compare the host galaxies of 902 supernovae, including SNe Ia, SNe II and SNe Ibc, which are selected by cross-matching the Asiago Supernova Catalog with the SDSS Data Release 7. We further selected 213 galaxies by requiring the light fraction of spectral observations $>$15%, which could represent well the global properties of the galaxies. Among them, 135 galaxies appear on the Baldwin-Phillips-Terlevich diagram, which allows us to compare the hosts in terms of star-forming, AGNs (including composites, LINERs and Seyfert 2s) and "Absorp" (their related emission-lines are weak or non-existence) galaxies. The diagrams related to parameters D$_n$(4000), H$\delta_A$, stellar masses, SFRs and specific SFRs for the SNe hosts show that almost all SNe II and most of SNe Ibc occur in SF galaxies, which have a wide range of stellar mass and low D$_n$(4000). The SNe Ia hosts as SF galaxies follow similar trends. A significant fraction of SNe Ia occurs in AGNs and Absorp galaxies, which are massive and have high D$_n$(4000). The stellar population analysis from spectral synthesis fitting shows that the hosts of SNe II have a younger stellar population than hosts of SNe Ia. These results are compared with those of the 689 comparison galaxies where the SDSS fiber captures less than 15% of the total light. These comparison galaxies appear biased towards higher 12+log(O/H) ($\sim$0.1dex) at a given stellar mass. Therefore, we believe the aperture effect should be kept in mind when the properties of the hosts for different types of SNe are discussed.Comment: 15 pages, 9 figure

Algebras of acyclic cluster type: tree type and type A~\widetilde{A}

In this paper, we study algebras of global dimension at most 2 whose generalized cluster category is equivalent to the cluster category of an acyclic quiver which is either a tree or of type $\widetilde{A}$. We are particularly interested in their derived equivalence classification. We prove that each algebra which is cluster equivalent to a tree quiver is derived equivalent to the path algebra of this tree. Then we describe explicitly the algebras of cluster type \A_n for each possible orientation of \A_n. We give an explicit way to read off in which derived equivalence class such an algebra lies, and describe the Auslander-Reiten quiver of its derived category. Together, these results in particular provide a complete classification of algebras which are cluster equivalent to tame acyclic quivers.Comment: v2: 37 pages. Title is changed. A mistake in the previous version is now corrected (see Remark 3.14). Other changes making the paper coherent with the version 2 of 1003.491