Invariant Differential Operators for Non-Compact Lie Groups: the Sp(n,R) Case

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras sp(n,R), in detail for n=6. Our choice of these algebras is motivated by the fact that they belong to a narrow class of algebras, which we call 'conformal Lie algebras', which have very similar properties to the conformal algebras of Minkowski space-time. We give the main multiplets and the main reduced multiplets of indecomposable elementary representations for n=6, including the necessary data for all relevant invariant differential operators. In fact, this gives by reduction also the cases for n<6, since the main multiplet for fixed n coincides with one reduced case for n+1.Comment: Latex2e, 27 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:0812.2690, arXiv:0812.265

The evolution of organizational niches : U.S. automobile manufacturers, 1885-1981.

Although the niche figures prominently in contemporary theories of organization, analysts often fail to tie micro processes within the niche to long-term changes in the broader environment. In this paper, we advance arguments about the relationship between an organization's niche and evolution in the structure of its organizational population over time. We focus on the technological niche and processes of positioning and crowding among firms in the niche space, relating them to the level of concentration among all firms in the market. Building on previous empirical studies in organizational ecology, we study the evolution of concentration in the American automobile industry from 1885 to 1981 and estimate models of the hazard of exit of individual producers from the market. The findings show that niche and concentration interact in complex ways, yielding a more unified depiction of organizational evolution than typically described or reported

Atypical Representations of Uq(sl(N))U_{q}(sl(N)) at Roots of Unity

We show how to adapt the Gelfand-Zetlin basis for describing the atypical representation of ${\cal U}_{\displaystyle{q}}(sl(N))$ when $q$ is root of unity. The explicit construction of atypical representation is presented in details for $N=3$.Comment: 18 pages, Tex-file and 2 figures. Uuencoded, compressed and tared archive of plain tex file and postscript figure file. Upon uudecoding, uncompressing and taring, tex the file atypique.te

No-Arbitrage Semi-Martingale Restrictions for Continuous-Time Volatility Models subject to Leverage Effects, Jumps and i.i.d. Noise: Theory and Testable Distributional Implications

We develop a sequential procedure to test the adequacy of jump-diffusion models for return distributions. We rely on intraday data and nonparametric volatility measures, along with a new jump detection technique and appropriate conditional moment tests, for assessing the import of jumps and leverage effects. A novel robust-to-jumps approach is utilized to alleviate microstructure frictions for realized volatility estimation. Size and power of the procedure are explored through Monte Carlo methods. Our empirical findings support the jump-diffusive representation for S&P500 futures returns but reveal it is critical to account for leverage effects and jumps to maintain the underlying semi-martingale assumption.

Explicit Character Formulae for Positive Energy UIRs of D=4 Conformal Supersymmetry

This paper continues the project of constructing the character formulae for the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). In the first paper we gave the bare characters which represent the defining odd entries of the characters. Now we give the full explicit character formulae for N=1 and for several important examples for N=2 and N=4.Comment: 48 pages, TeX with Harvmac, overlap in preliminaries with arXiv:hep-th/0406154; some comments and references adde

On a "New" Deformation of GL(2)

We refute a recent claim in the literature of a "new" quantum deformation of GL(2).Comment: 4 pages, LATE

Exotic Bialgebra S03: Representations, Baxterisation and Applications

The exotic bialgebra S03, defined by a solution of the Yang-Baxter equation, which is not a deformation of the trivial, is considered. Its FRT dual algebra $s03_F$ is studied. The Baxterisation of the dual algebra is given in two different parametrisations. The finite-dimensional representations of $s03_F$ are considered. Diagonalisations of the braid matrices are used to yield remarkable insights concerning representations of the L-algebra and to formulate the fusion of finite-dimensional representations. Possible applications are considered, in particular, an exotic eight-vertex model and an integrable spin-chain model.Comment: 24 pages, Latex; V2: revised subsection 4.1, added 9 references, to appear in Annales Henri Poincare in the volume dedicated to D. Arnaudo