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

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

Irreducible Characters of General Linear Superalgebra and Super Duality

We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical Kazhdan-Lusztig theory. We further verify a parabolic version of a conjecture of Brundan on the irreducible characters in the BGG category \mc{O} of the general linear superalgebra. We also prove the super duality conjecture

Super duality and irreducible characters of ortho-symplectic Lie superalgebras

We formulate and establish a super duality which connects parabolic categories $O$ between the ortho-symplectic Lie superalgebras and classical Lie algebras of $BCD$ types. This provides a complete and conceptual solution of the irreducible character problem for the ortho-symplectic Lie superalgebras in a parabolic category $O$, which includes all finite-dimensional irreducible modules, in terms of classical Kazhdan-Lusztig polynomials.Comment: 30 pages, Section 5 rewritten and shortene

Characters of the Positive Energy UIRs of D=4 Conformal Supersymmetry

We give character formulae for the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). Using these we also derive decompositions of long superfields as they descend to the unitarity threshold. These results are also applicable to irreps of the complex Lie superalgebras sl(4/N). Our derivations use results from the representation theory of su(2,2/N) developed already in the 80s.Comment: 81 pages, input files: harvmac, amssym.def, amssym.tex; corrected presentation on odd reflection