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Schubert Derivations are distinguished instances of Higher Order
(or Hasse-Schmidt) derivations on exterior algebras [8], originally introduced
to phrase Schubert Calculus for Grassmannians varieties, solely in terms of
Leibniz rules and integration by parts.
The purpose of the talk is showing their applications to find explicit vertex operators representations of Lie algebras of endomorphisms on exterior
algebras and related spaces [1, 2, 3, 4], like the infinite wedge power (as in
[9] and the bosonic Fock space (a polynomial ring in infinitely many indeterminates). This is related with some pioneering work done by Date, Jimbo,
kashiwara and Miwa at the beginning of the Eighties [5].
The premises are the following two elementary observations: each vector
space is a representation of the Lie algebra of its own endomorphisms and the
r-th exterior power of a polynomial ring in one indeterminate is isomorphic
to a polynomial ring in r indeterminates.
References
[1] O. Behzad, Hasse-Schmidt Derivations and Vertex Operators on Exterior Algebras. Ph.D. Thesis, IASBS, Zanjan, 2021;
[2] O. Behzad, A. Contiero, L. Gatto, R. Vidal Martins, Polynomial
ring representation of endomorphisms of exterior powers. Collectanea
Math., 2021 (to appear), ArXiv:2005.01154.pdf,
[3] O. Behzad, L. Gatto, Bosonic and Fermionic Representations of Endomorphisms of Exterior Algebras, Fundamenta Math. 2021 (to appear),
ArXiv:2009.00479.pdf
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Meeting ID: 929 970 0405
Passcode: 210406
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