2 00 9 Pieri resolutions for classical groups
نویسندگان
چکیده
We generalize the constructions of Eisenbud, Fløystad, and Weyman for equivariant minimal free resolutions over the general linear group, and we construct equivariant resolutions over the orthogonal and symplectic groups. We also conjecture and provide some partial results for the existence of an equivariant analogue of Boij–Söderberg decompositions for Betti tables, which were proven to exist in the non-equivariant setting by Eisenbud and Schreyer. Many examples are given.
منابع مشابه
4 M ay 2 00 9 An ( inverse ) Pieri formula for Macdonald polynomials of type C Michel
We give an explicit Pieri formula for Macdonald polynomials attached to the root system Cn (with equal multiplicities). By inversion we obtain an explicit expansion for two-row Macdonald polynomials of type C.
متن کاملDouble Pieri Algebras and Iterated Pieri Algebras for the Classical Groups
We study iterated Pieri rules for representations of classical groups. That is, we consider tensor products of a general representation with multiple factors of representations corresponding to one-rowed Young diagrams (or in the case of the general linear group, also the duals of these). We define iterated Pieri algebras, whose structure encodes the irreducible decompositions of such tensor pr...
متن کاملPieri-type Formulas for Maximal Isotropic Grassmannians via Triple Intersections
We give an elementary proof of the Pieri-type formula in the cohomology of a Grassmannian of maximal isotropic subspaces of an odd orthogonal or symplectic vector space. This proof proceeds by explicitly computing a triple intersection of Schubert varieties. The decisive step is an exact description of the intersection of two Schubert varieties, from which the multiplicities (which are powers o...
متن کاملPieri Rules for Classical Groups and Equinumeration between Generalized Oscillating Tableaux and Semistandard Tableaux
We present several equinumerous results between generalized oscillating tableaux and semistandard tableaux and give a representation-theoretic proof to them. As one of the key ingredients of the proof, we provide Pieri rules for the symplectic and orthogonal groups.
متن کاملeb 2 00 4 Inversion of the Pieri formula for Macdonald polynomials
We give the explicit analytic development of Macdonald polynomials in terms of “modified complete” and elementary symmetric functions. These expansions are obtained by inverting the Pieri formula. Specialization yields similar developments for monomial, Jack and Hall–Littlewood symmetric functions. ∗The second author was fully supported by an APART fellowship of the Austrian Academy of Sciences...
متن کامل