Q-identities and Affinized Projective Varieties Ii. Flag Varieties
نویسندگان
چکیده
In a previous paper we defined the concept of an affinized projective variety and its associated Hilbert series. We computed the Hilbert series for varieties associated to quadratic monomial ideals. In this paper we show how to apply these results to affinized flag varieties. We discuss various examples and conjecture a correspondence between the Hilbert series of an affinized flag variety and a modified Hall-Littlewood polynomial. We briefly discuss the application of these results to quasi-particle character formulas for affine Lie algebra modules.
منابع مشابه
q-IDENTITIES AND AFFINIZED PROJECTIVE VARIETIES I. QUADRATIC MONOMIAL IDEALS
We define the concept of an affinized projective variety and show how one can, in principle, obtain q-identities by different ways of computing the Hilbert series of such a variety. We carry out this program for projective varieties associated to quadratic monomial ideals. The resulting identities have applications in describing systems of quasi-particles containing null-states and can be inter...
متن کاملQuiver Flag Varieties and Multigraded Linear Series
This paper introduces a class of smooth projective varieties that generalise and share many properties with partial flag varieties of type A. The quiver flag variety Mθ(Q, r) of a finite acyclic quiver Q (with a unique source) and a dimension vector r is a fine moduli space of stable representations of Q. Quiver flag varieties are Mori Dream Spaces, they are obtained via a tower of Grassmann bu...
متن کاملChow Flag Variety and Lawson Homology
The Chow flag varieties are introduced and studied. In a family of pure dimensional projective complex varieties defined via Chow flag varieties, the isomorphism type of Lawson homology of a general member in the family is discussed. Applications to morphic cohomology and motivic cohomology on smooth projective complex varieties are discussed.
متن کاملLectures on the geometry of flag varieties
In these notes, we present some fundamental results concerning flag varieties and their Schubert varieties. By a flag variety, we mean a complex projective algebraic variety X, homogeneous under a complex linear algebraic group. The orbits of a Borel subgroup form a stratification of X into Schubert cells. These are isomorphic to affine spaces; their closures in X are the Schubert varieties, ge...
متن کاملSCHUBERT UNIONS AND CODES ON l - STEP FLAG VARIETIES
— In Section 1 we define and study Schubert unions on l-step flag varieties. This has previously been done in the Grassmann case, i.e., the l = 1 case, by Hansen, Johnsen and Ranestad [7]. In Section 2 we study the algebraic codes given by mapping l-step flag varieties into projective space. This subject has also been treated in the Grassmann case previously (see p. 52). Résumé (Unions de cellu...
متن کامل