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The Fine Moduli Space of Representations of Clifford Algebras
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Date
2011-01-01
Author
Coşkun, Emre
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Given a fixed binary form f(u,v) of degree d over a field k, the associated Clifford algebra is the k-algebra C(f)=k{u,v}/I, where I is the two-sided ideal generated by elements of the form (alpha u+beta v)(d)-f(alpha,beta) with alpha and beta arbitrary elements in k. All representations of C(f) have dimensions that are multiples of d, and occur in families. In this article, we construct fine moduli spaces U=U(f,r) for the irreducible rd-dimensional representations of C(f) for each r >= 2. Our construction starts with the projective curve C subset of P(k)(2) defined by the equation w(d) = f(u, v), and produces U(f,r) as a quasiprojective variety in the moduli space M(r, d(r))of stable vector bundles over C with rank r and degree d(r)=r(d+g-1), where g denotes the genus of C.
Subject Keywords
General Mathematics
URI
https://hdl.handle.net/11511/43325
Journal
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
DOI
https://doi.org/10.1093/imrn/rnq221
Collections
Department of Mathematics, Article
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E. Coşkun, “The Fine Moduli Space of Representations of Clifford Algebras,”
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
, pp. 3524–3559, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/43325.