A Selberg integral for the Lie algebra A_n

A new q-binomial theorem for Macdonald polynomials is employed to prove an A_n analogue of the celebrated Selberg integral. This confirms the g=A_n case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral for every simple Lie algebra g.Comment: 32 page

ABCD of Beta Ensembles and Topological Strings

We study beta-ensembles with Bn, Cn, and Dn eigenvalue measure and their relation with refined topological strings. Our results generalize the familiar connections between local topological strings and matrix models leading to An measure, and illustrate that all those classical eigenvalue ensembles, and their topological string counterparts, are related one to another via various deformations and specializations, quantum shifts and discrete quotients. We review the solution of the Gaussian models via Macdonald identities, and interpret them as conifold theories. The interpolation between the various models is plainly apparent in this case. For general polynomial potential, we calculate the partition function in the multi-cut phase in a perturbative fashion, beyond tree-level in the large-N limit. The relation to refined topological string orientifolds on the corresponding local geometry is discussed along the way.Comment: 33 pages, 1 figur

Ontogeny of central serotonergic neurons in the directly developing frog, Eleutherodactylus coqui

Embryonic development of the central serotonergic neurons in the directly developing frog, Eleutherodactylus coqui , was determined by using immunocytochemistry. The majority of anuran amphibians (frogs) possess a larval stage (tadpole) that undergoes metamorphosis, a dramatic post-embryonic event, whereby the tadpole transforms into the adult phenotype. Directly developing frogs have evolved a derived life-history mode where the tadpole stage has been deleted and embryos develop directly into the adult bauplan. Embryonic development in E. coqui is classified into 15 stages (TS 1–15; 1 = oviposition / 15 = hatching). Serotonergic immunoreactivity was initially detected at TS 6 in the raphe nuclei in the developing rhombencephalon. At TS 7, immunopositive perikarya were observed in the paraventricular organ in the hypothalamus and reticular nuclei in the hindbrain. Development of the serotonergic system was steady and gradual during mid-embryogenesis. However, starting at TS 13 there was a substantial increase in the number of serotonergic neurons in the paraventricular, raphe, and reticular nuclei, a large increase in the number of varicose fibers, and a differentiation of the reticular nuclei in the hindbrain. Consequentially, E. coqui displayed a well-developed central serotonergic system prior to hatching (TS 15). In comparison, the serotonergic system in metamorphic frogs typically starts to develop earlier but the surge of development that transpires in this system occurs post-embryonically, during metamorphosis, and not in the latter stages of embryogenesis, as it does in E. coqui . Overall, the serotonergic development in E. coqui is similar to the other vertebrates.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47526/1/429_2005_Article_22.pd

On the elliptic nonabelian Fourier transform for unipotent representations of p-adic groups

In this paper, we consider the relation between two nonabelian Fourier transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig parameters for unipotent elliptic representations of a split p-adic group and the second is defined in terms of the pseudocoefficients of these representations and Lusztig's nonabelian Fourier transform for characters of finite groups of Lie type. We exemplify this relation in the case of the p-adic group of type G_2