Semi-infinite Plücker Relations and Weyl Modules

The goal of this paper is two-fold. First, we write down the semi-infinite Plücker relations, describing the Drinfeld–Plücker embedding of the (formal version of) semi-infinite flag varieties in type A. Second, we study the homogeneous coordinate ring, that is, the quotient by the ideal generated by the semi-infinite Plücker relations. We establish the isomorphism with the algebra of dual global Weyl modules and derive a new character formula.

[1]  Syu Kato,et al.  Equivariant K -theory of semi-infinite flag manifolds and the Pieri–Chevalley formula , 2017, Duke Mathematical Journal.

[2]  Syu Kato,et al.  Pieri-Chevalley type formula for equivariant $K$-theory of semi-infinite flag manifolds , 2017 .

[3]  Syu Kato.  Demazure character formula for semi-infinite flag manifolds , 2016 .

[4]  Evgeny Feigin,et al.  Nonsymmetric Macdonald polynomials and PBW filtration: Towards the proof of the Cherednik-Orr conjecture , 2015, J. Comb. Theory, Ser. A.

[5]  Michael Finkelberg,et al.  Twisted zastava and q ‐Whittaker functions , 2014, J. Lond. Math. Soc..

[6]  M. Finkelberg,et al.  Weyl modules and $$q$$q-Whittaker functions , 2012, 1203.1583.

[7]  M. Finkelberg,et al.  Semi-infinite Schubert varieties and quantum K-theory of flag manifolds , 2011, 1111.2266.

[8]  B. Ion,et al.  BGG reciprocity for current algebras , 2011, Compositio Mathematica.

[9]  Katsuyuki Naoi.  Weyl modules, Demazure modules and finite crystals for non-simply laced type , 2010, 1012.5480.

[10]  Evgeny Feigin,et al.  PBW filtration and bases for symplectic Lie algebras , 2010, 1010.2321.

[11]  Evgeny Feigin,et al.  PBW filtration and bases for irreducible modules in type An , 2010, 1002.0674.

[12]  G. Fourier,et al.  A categorical approach to Weyl modules , 2009, 0906.2014.

[13]  S. Loktev,et al.  Weyl, Demazure and fusion modules for the current algebra of sl r+1 , 2006 .

[14]  N. Loehr,et al.  A combinatorial formula for non-symmetric Macdonald polynomials , 2006, math/0601693.

[15]  G. Fourier,et al.  Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions , 2005, math/0509276.

[16]  G. Fourier,et al.  Tensor Product Structure of Affine Demazure Modules and Limit Constructions , 2004, Nagoya Mathematical Journal.

[17]  Shrawan Kumar,et al.  Kac-Moody Groups, their Flag Varieties and Representation Theory , 2002 .

[18]  B. Ion.  Nonsymmetric Macdonald polynomials and Demazure characters , 2001, math/0105061.

[19]  M. Mustaţǎ,et al.  Jet schemes of locally complete intersection canonical singularities , 2000, math/0008002.

[20]  Yasmine B. Sanderson.  On the Connection Between Macdonald Polynomials and Demazure Characters , 2000 .

[21]  A. Pressley,et al.  Weyl modules for classical and quantum affine algebras , 2000, math/0004174.

[22]  D. Gaitsgory,et al.  Geometric Eisenstein series , 1999 .

[23]  M. Finkelberg,et al.  Semiinfinite Flags. I. Case of global curve $P^1$ , 1997, alg-geom/9707010.

[24]  W. Fulton.  Young Tableaux: With Applications to Representation Theory and Geometry , 1996 .

[25]  N. Loehr,et al.  A Combinatorial Formula for Nonsymmetric Macdonald Polynomials , 2008 .

[26]  Moritz Beckmann,et al.  Young tableaux , 2007 .

[27]  I. G. MacDonald,et al.  Affine Hecke Algebras and Orthogonal Polynomials , 2003 .

[28]  Basic Theory,et al.  Kac-Moody Groups , 2002 .

[29]  Ivan Cherednik,et al.  Nonsymmetric Macdonald polynomials , 1995 .