Quantum multiplication operators for Lagrangian and orthogonal Grassmannians
نویسندگان
چکیده
منابع مشابه
Quantum Cohomology of Orthogonal Grassmannians
Let V be a vector space with a nondegenerate symmetric form and OG be the orthogonal Grassmannian which parametrizes maximal isotropic subspaces in V . We give a presentation for the (small) quantum cohomology ring QH∗(OG) and show that its product structure is determined by the ring of P̃ -polynomials. A ‘quantum Schubert calculus’ is formulated, which includes quantum Pieri and Giambelli formu...
متن کاملQuantum Cohomology Rings of Lagrangian and Orthogonal Grassmannians and Total Positivity
We verify in an elementary way a result of Peterson for the maximal orthogonal and Lagrangian Grassmannians, and then find Vafa-Intriligator type formulas which compute their 3-point, genus zero Gromov-Witten invariants. Finally we study the total positivity of the related Peterson’s varieties and show that Rietsch’s conjecture about the total positivity holds for these cases.
متن کاملQuantum Cohomology Rings of Lagrangian and Orthogonal Grassmannians and Vafa-intriligator Type Formulas
We verify in an elementary way a result of Peterson for the maximal orthogonal and Lagrangian Grassmannians, and then find Vafa-Intriligator type formulas which compute their 3point, genus zero Gromov-Witten invariants. Additionally, we study total positivity of the related Peterson varieties and investigate its relationship with the positivity of Schubert basis elements.
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متن کاملIncompressibility of Orthogonal Grassmannians
We prove the following conjecture due to Bryant Mathews (2008). Let Q be the orthogonal grassmannian of totally isotropic i-planes of a non-degenerate quadratic form q over an arbitrary field (where i is an integer satisfying 1 ≤ i ≤ (dim q)/2). If the degree of each closed point on Q is divisible by 2 and the Witt index of q over the function field of Q is equal to i, then the variety Q is 2-i...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2017
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-017-0737-7