The 6-vertex model and deformations of the Weyl character formula

We use statistical mechanics -- variants of the six-vertex model in the plane studied by means of the Yang-Baxter equation -- to give new deformations of Weyl's character formula for classical groups of Cartan type B, C, and D, and a character formula of Proctor for type BC. In each case, the corresponding Boltzmann weights are associated to the free fermion point of the six-vertex model. These deformations add to the earlier known examples in types A and C by Tokuyama and Hamel-King, respectively. A special case for classical types recovers deformations of the Weyl denominator formula due to Okada.Comment: v2: renamed the last family of models and showed their connection to character formulae for groups of type BC; addressed some issues in the proof of Lemma 6.2; updated abstrac

Galois module structure of Galois cohomology for embeddable cyclic extensions of degree p^n

Let p>2 be prime, and let n,m be positive integers. For cyclic field extensions E/F of degree p^n that contain a primitive pth root of unity, we show that the associated F_p[Gal(E/F)]-modules H^m(G_E,mu_p) have a sparse decomposition. When E/F is additionally a subextension of a cyclic, degree p^{n+1} extension E'/F, we give a more refined F_p[Gal(E/F)]-decomposition of H^m(G_E,mu_p)