Drinfeld Functor and Finite-Dimensional Representations of Yangian

We extend the results of Drinfeld on Drinfeld functor to the case l>n. We present the character of finite-dimensional representations of the Yangian Y(sl_n) in terms of the Kazhdan-Lusztig polynomials as a consequence.Comment: Latex2e, 17pages, corrected typo

Rationality of admissible affine vertex algebras in the category O

We study the vertex algebras associated with modular invariant representations of affine Kac-Moody algebras at fractional levels, whose simple highest weight modules are classified by Joseph's characteristic varieties. We show that an irreducible highest weight representation of a non-twisted affine Kac-Moody algebra at an admissible level k is a module over the associated simple affine vertex algebra if and only if it is an admissible representation whose integral root system is isomorphic to that of the vertex algebra itself. This in particular proves the conjecture of Adamovic and Milas on the rationality of admissible affine vertex algebras in the category O.Comment: Improved exposition, to appear in Duke Math.

Research into food preservation using a bacteriocin produced by Lactobacillus gasseri

Bacteriocins are natural antibacterial peptides ribosomally biosynthesized by bacteria. Gassericin T which is a bacteriocin produced by many strains of Lactobacillus gasseri has a broad antibacterial spectrum against food spoilage and pathogenic Gram-positive bacteria; therefore, the bacteriocin and its producers are predicted for use as safe food preservatives. However, probiotic Lb. gasseri strains show poor growth and minimally produce gassericin T in food-grade natural media such as reconstituted cheese whey, unlike in MRS broth. The growth of Lb. gasseri in reconstituted cheese whey was improved by adding proteose peptone as a nutrient factor. The production of gassericin T in MRS broth was specifically inhibited by adding divalent metal cations, and then the inhibition was removed using a chelator of divalent cations, trisodium citrate dihydrate. The production of gassericin T in reconstituted cheese whey was also restored by adding trisodium citrate dihydrate, and the activity was enhanced by a surfactant, Tween 80. In addition, trisodium citrate dihydrate led to over-production of and synergistic antibacterial effect with gassericin T. In this study, we developed a cheese whey-based medium containing proteose peptone, trisodium citrate dihydrate and Tween 80 for gassericin T production. The developed food-grade medium may contribute to the effective use of some bacteriocins from probiotic lactic acid bacteria for biopreservation of foods

Two-sided BGG resolutions of admissible representations

We prove the conjecture of Frenkel, Kac and Wakimoto on the existence of two-sided BGG resolutions of G-integrable admissible representations of affine Kac-Moody algebras at fractional levels. As an application we establish the semi-infintie analogue of the generalized Borel-Weil theorem for mimimal parabolic subalgebras which enables an inductive study of admissible representations.Comment: revised, to appear in Representation Theor