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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
, 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 .Comment: 34 pages. To appear in Israel J. of Mat
Algebras of acyclic cluster type: tree type and type
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 . 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
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
ABC-type estimates via Garsia-type norms
We are concerned with extensions of the Mason--Stothers theorem from
polynomials to analytic functions on the unit disk . The new feature
is that the number of zeros of a function in gets replaced by
the norm of the associated Blaschke product in a suitable smoothness
space . Such extensions are shown to exist, and the appropriate -type
estimates are exhibited, provided that admits a "Garsia-type norm", i.e., a
norm sharing certain properties with the classical Garsia norm on BMO. Special
emphasis is placed on analytic Lipschitz spaces.Comment: 9 page
Branes in type 0/type II duality
We derive relations between type 0 and type II D-brane configurations under
the T-duality suggested by Bergman and Gaberdiel and confirm that the massless
fields on D-branes are identical to those on the dual D-brane configurations.
Furthermore, we discuss dualities of type 0 and type II NS5-branes and find
that the dual of an unwrapped type 0 NS5-brane is a Kaluza-Klein monopole with
non-supersymmetric blow up modes.Comment: 11 pages, 2 figures, explanations added, typos correcte
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