On the Hall Algebra of an Elliptic Curve, Ii
نویسنده
چکیده
was described in terms of the so-called Hall algebra U+X of the category of coherent sheaves on an elliptic curve X (defined over a finite field Fq). This Hall algebra turns out to be a two-parameter deformation of ΛΛ, the two deformation parameters being the Frobenius eigenvalues σ, σ̄ of the particular elliptic curve. In fact, the structure constants for U+X are Laurent polynomials in σ and σ̄, and U+X is the specialization of some “universal” Hall algebra E + R defined over the ring R = C[σ, σ̄]. This provides a generalization, to the rings of diagonal invariants, of Steinitz and Hall’s well-known realization of the ring of symmetric functions in terms of the classical Hall algebra (see [M], Chap.II).
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