Global analysis by hidden symmetry

Hidden symmetry of a G'-space X is defined by an extension of the G'-action on X to that of a group G containing G' as a subgroup. In this setting, we study the relationship between the three objects: (A) global analysis on X by using representations of G (hidden symmetry); (B) global analysis on X by using representations of G'; (C) branching laws of representations of G when restricted to the subgroup G'. We explain a trick which transfers results for finite-dimensional representations in the compact setting to those for infinite-dimensional representations in the noncompact setting when $X_C$ is $G_C$-spherical. Applications to branching problems of unitary representations, and to spectral analysis on pseudo-Riemannian locally symmetric spaces are also discussed.Comment: Special volume in honor of Roger Howe on the occasion of his 70th birthda

Smart-Cut Layer Transfer of Single-Crystal SiC Using Spin-on-Glass

The authors demonstrate “smart-cut”-type layer transfer of single-crystal silicon carbide (SiC) by using spin-on-glass (SoG) as an adhesion layer. Using SoG as an adhesion layer is desirable because it can planarize the surface, facilitate an initial low temperature bond, and withstand the thermal stresses at high temperature where layer splitting occurs (800–900 °C). With SoG, the bonding of wafers with a relatively large surface roughness of 7.5–12.5 Å rms can be achieved. This compares favorably to direct (fusion) wafer bonding, which usually requires extremely low roughness (\u3c2 Å rms), typically achieved using chemical mechanical polishing (CMP) after implantation. The higher roughness tolerance of the SoG layer transfer removes the need for the CMP step, making the process more reliable and affordable for expensive materials like SiC. To demonstrate the reliability of the smart-cut layer transfer using SoG, we successfully fabricated a number of suspended MEMS structures using this technology

Small representations of finite classical groups

Finite group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of representations of the group. In particular, the representations of small dimensions tend to contribute the largest terms to these sums, so a systematic knowledge of these small representations could lead to proofs of important conjectures which are currently out of reach. Despite the classification by Lusztig of the irreducible representations of finite groups of Lie type, it seems that this aspect remains obscure. In this note we develop a language which seems to be adequate for the description of the "small" representations of finite classical groups and puts in the forefront the notion of rank of a representation. We describe a method, the "eta correspondence", to construct small representations, and we conjecture that our construction is exhaustive. We also give a strong estimate on the dimension of small representations in terms of their rank. For the sake of clarity, in this note we describe in detail only the case of the finite symplectic groups.Comment: 18 pages, 9 figures, accepted for publications in the proceedings of the conference on the occasion of Roger Howe's 70th birthday (1-5 June 2015, Yale University, New Haven, CT

A Model for Emission Yield from Planar Photocathodes Based on Photon-Enhanced Thermionic Emission or Negative-Electron-Affinity Photoemission

A general model is presented for electron emission yield from planar photocathodes that accounts for arbitrary cathode thickness and finite recombination velocities at both front and back surfaces. This treatment is applicable to negative electron affinity emitters as well as positive electron affinity cathodes, which have been predicted to be useful for energy conversion. The emission model is based on a simple one-dimensional steady-state diffusion treatment. The resulting relation for electron yield is used to model emission from thin-film cathodes with material parameters similar to GaAs. Cathode thickness and recombination at the emissive surface are found to strongly affect emission yield from cathodes, yet the magnitude of the effect greatly depends upon the emission mechanism. A predictable optimal film thickness is found from a balance between optical absorption, surface recombination, and emission rate