1,804 research outputs found
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)
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