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Pfaffians and Shuffling Relations for the Spin Module

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Abstract

We present explicit formulas for a set of generators of the ideal of relations among the pfaffians of the principal minors of the antisymmetric matrices of fixed dimension. These formulas have an interpretation in terms of the standard monomial theory for the spin module of orthogonal groups.

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References

  1. Chirivì, R., Littelmann, P., Maffei, A.: Equations defining symmetryc varieties and affine Grassmannians. I.M.R.N. 2009(2), 291–347 (2009)

    MATH  Google Scholar 

  2. Hodge, W.V.D.: Some enumerative results in the theory of forms. Proc. Cambridge Philos. Soc. 39, 22–30 (1943)

    Article  MathSciNet  MATH  Google Scholar 

  3. Humphreys, J.E.: Reflection Groups and Coxeter Groups. Cambridge Studies in Advanced Mathematics, vol. 29, Cambridge University Press, Cambridge (2009)

    Google Scholar 

  4. Kustin, A.R.: Pfaffian identities, with applications to free resolutions, DG–algebras, and algebras with straightening law. Commutative algebra: syzygies, multiplicities and birational algebra. Contemp. Math. 159, 269–292 (1994)

    Article  MathSciNet  Google Scholar 

  5. Seshadri, C.S.: Geometry of G/P. I. Theory of standard monomials for minuscule representations. In: C.P. Ramanujam—A Tribute. Tata Inst. Fund. Res. Studies in Math., vol. 8, pp. 207–239 (1978)

  6. Seshadri, C.S.: Standard monomial theory and the work of Demazure. Algebraic varieties and analytic varieties. Adv. Stud. Pure Math. 1, 355–384 (1983)

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dip. di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy

    Rocco Chirivì & Andrea Maffei

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  1. Rocco Chirivì
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  2. Andrea Maffei
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Correspondence to Rocco Chirivì.

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Chirivì, R., Maffei, A. Pfaffians and Shuffling Relations for the Spin Module. Algebr Represent Theor 16, 955–978 (2013). https://doi.org/10.1007/s10468-012-9341-7

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  • DOI: https://doi.org/10.1007/s10468-012-9341-7

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