A new set of realizations of the Virasoro algebra on a bosonic Fock space are found by explicitly computing the Virasoro representations associated with coadjoint orbits of the form DiffS 1 /S 1. Some progress is made in understanding the unitary structure of these representations. The characters of these representations are exactly the bosonic partition functions calculated previously by Witte...

WC. Trans fatty acids and cardiovascular disease. N Engl J Med 2006;354:1601–13. 31. Vinson JA, Cai Y. Nuts, especially walnuts, have both antioxidant quantity and efficacy and exhibit significant potential health benefits. Food Function 2012;3:134–40. 32. Blomhoff R, Carlsen MH, Andersen LF, Jacobs DR Jr. Health benefits of nuts: potential role of antioxidants. Br J Nutr 2006;96(Suppl 2):S52–6...

Recursively-constructed couplings have been used in the past for mixing on trees. We show how to extend this technique to non-tree-like graphs such as lattices. Using this method, we obtain the following general result. Suppose that G is a triangle-free graph and that for some Δ ≥ 3, the maximum degree of G is at most Δ. We show that the spin system consisting of q-colourings of G has strong sp...