Universal characters twisted by roots of unity

A classical result of Littlewood gives a factorisation for the Schur function at a set of variables "twisted" by a primitive $t$-th root of unity, characterised by the core and quotient of the indexing partition. While somewhat neglected, it has proved to be an important tool in the character theory of the symmetric group, the cyclic sieving phenomenon, plethysms of symmetric functions and more. Recently, similar factorisations for the characters of the groups $\mathrm{O}(2n,\mathbb{C})$, $\mathrm{Sp}(2n,\mathbb{C})$ and $\mathrm{SO}(2n+1,\mathbb{C})$ were obtained by Ayyer and Kumari. We lift these results to the level of universal characters, which has the benefit of making the proofs simpler and the structure of the factorisations more transparent. Our approach also allows for universal character extensions of some factorisations of a different nature originally discovered by Ciucu and Krattenthaler, and generalised by Ayyer and Behrend.Comment: 23 pages; minor changes, a few new references, to appear in Algebraic Combinatoric

Blue Hill Shipping Receipt: Clara Norton, March 1862

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Brooksville Shipping Receipt: Clara Norton, October 1861

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Blue HillShipping Receipt: Clara Norton, April 1861

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Blue Hill Shipping Receipt: Clara Norton, September 1861

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Blue Hill Shipping Receipt: Clara Norton, October 1862

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Teaching Teachers for the Future (TTF) Project: Development of the TTF TPACK survey instrument

This paper presents a summary of the key findings of the TTF TPACK Survey developed and administered for the Teaching the Teachers for the Future (TTF) Project implemented in 2011. The TTF Project, funded by an Australian Government ICT Innovation Fund grant, involved all 39 Australian Higher Education Institutions which provide initial teacher education. TTF data collections were undertaken at the end of Semester 1 (T1) and at the end of Semester 2 (T2) in 2011. A total of 12881 participants completed the first survey (T1) and 5809 participants completed the second survey (T2). Groups of like-named items from the T1 survey were subject to a battery of complementary data analysis techniques. The psychometric properties of the four scales: Confidence - teacher items; Usefulness - teacher items; Confidence - student items; Usefulness- student items, were confirmed both at T1 and T2. Among the key findings summarised, at the national level, the scale: Confidence to use ICT as a teacher showed measurable growth across the whole scale from T1 to T2, and the scale: Confidence to facilitate student use of ICT also showed measurable growth across the whole scale from T1 to T2. Additional key TTF TPACK Survey findings are summarised

Blue Hill Shipping Receipt: Clara Norton, June 1863

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Dauphine Was Right: Masques, the Authenticity of (Un)Performed Identity, and the Two Prologues of Epicene

This paper argues that Epicene, Jonson's first public play after being made official court masque writer, is unusually optimistic about the possibilities of drama. The play explores the possibility of creating an authentic personality through performance, an idea that Jonson is often hostile towards. However, Jonson's flirtation with this pro-theater perspective was short lived. For complex reasons, Lady Arbella's complaint about the play led Jonson to once again grow cynical about the possibilities of the public stage. These vacillating perspectives, I argue, can be traced within the two different prologues, which offer two very different perspectives on playing, play going and the theater

On the Matrix Description of Calabi-Yau Compactifications

We point out that the matrix description of M-theory compactified on Calabi-Yau threefolds is in many respects simpler than the matrix description of a $T^6$ compactification. This is largely because of the differences between D6 branes wrapped on Calabi-Yau threefolds and D6 branes wrapped on six-tori. In particular, if we define the matrix theory following the prescription of Sen and Seiberg, we find that the remaining degrees of freedom are decoupled from gravity.Comment: 12 pages, harvmac big; comment on 4d N=1 theories change