Highest weight modules over quantum queer Lie superalgebra U_q(q(n))

In this paper, we investigate the structure of highest weight modules over the quantum queer superalgebra $U_q(q(n))$. The key ingredients are the triangular decomposition of $U_q(q(n))$ and the classification of finite dimensional irreducible modules over quantum Clifford superalgebras. The main results we prove are the classical limit theorem and the complete reducibility theorem for $U_q(q(n))$-modules in the category $O_q^{\geq 0}$.Comment: Definition 1.5 and Definition 6.1 are changed, and a remark is added in the new versio

Bott - Borel - Weil Construction For Quantum Supergroup Uq(gl(m|n))

The finite dimensional irreducible representations of the quantum supergroup $U_q(gl(m|n))$ are constructed geometrically using techniques from the Bott - Borel - Weil theory and vector coherent states.Comment: Latex, 22 page

Tensor representations of Mackey Lie algebras and their dense subalgebras

In this article we review the main results of the earlier papers [PStyr, PS] and [DPS], and establish related new results in considerably greater generality. We introduce a class of infinite-dimensional Lie algebras gM, which we call Mackey Lie algebras, and define monoidal categories TgM of tensor gM-modules. We also consider dense subalgebras a⊂gM and corresponding categories Ta. The locally finite Lie algebras sl(V,W),o(V),sp(V) are dense subalgebras of respective Mackey Lie algebras. Our main result is that if gM is a Mackey Lie algebra and a⊂gM is a dense subalgebra, then the monoidal category Ta is equivalent to Tsl(∞) or To(∞); the latter monoidal categories have been studied in detail in [DPS]. A possible choice of a is the well-known Lie algebra of generalized Jacobi matrices

An algebraic-geometric construction of ind-varieties of generalized flags

We define the class of admissible linear embeddings of flag varieties. The definition is given in the general language of algebraic geometry. We then prove that an admissible linear embedding of flag varieties has a certain explicit form in terms of linear algebra. This result enables us to show that any direct limit of admissible embeddings of flag varieties is isomorphic to an ind-variety of generalized flags as defined in [DP]. These latter ind-varieties have been introduced in terms of the ind-group SL(\infty) (respectively, O(\infty) or Sp(\infty) for isotropic generalized flags), and the current paper constructs them in purely algebraic-geometric term

The return of the bursts: Thermonuclear flashes from Circinus X-1

We report the detection of 15 X-ray bursts with RXTE and Swift observations of the peculiar X-ray binary Circinus X-1 during its May 2010 X-ray re-brightening. These are the first X-ray bursts observed from the source after the initial discovery by Tennant and collaborators, twenty-five years ago. By studying their spectral evolution, we firmly identify nine of the bursts as type I (thermonuclear) X-ray bursts. We obtain an arcsecond location of the bursts that confirms once and for all the identification of Cir X-1 as a type I X-ray burst source, and therefore as a low magnetic field accreting neutron star. The first five bursts observed by RXTE are weak and show approximately symmetric light curves, without detectable signs of cooling along the burst decay. We discuss their possible nature. Finally, we explore a scenario to explain why Cir X-1 shows thermonuclear bursts now but not in the past, when it was extensively observed and accreting at a similar rate.Comment: Accepted for publication in The Astrophysical Journal Letters. Tables 1 & 2 merged. Minor changes after referee's comments. 5 pages, 4 Figure