Affine PBW bases and affine MV polytopes
نویسندگان
چکیده
منابع مشابه
Rank 2 Affine Mv Polytopes
We give a realization of the crystal B(−∞) for ̂ sl2 using decorated polygons. The construction and proof are combinatorial, making use of Kashiwara and Saito’s characterization of B(−∞), in terms of the ∗ involution. The polygons we use have combinatorial properties suggesting they are the ̂ sl2 analogues of the Mirković-Vilonen polytopes defined by Anderson and the third author in finite type. ...
متن کاملMv-polytopes via Affine Buildings
For an algebraic group G, Anderson originally defined the notion of MV-polytopes in [And03], images of MV-cycles, defined in [MV07], under the moment map of the corresponding affine Grassmannian. It was shown by Kamnitzer in [Kam07] and [Kam05] that these polytopes can be described via tropical relations and give rise to a crystal structure on the set of MV-cycles. Another crystal structure can...
متن کاملConvex Bases of Pbw Type for Quantum Affine Algebras
This note has two purposes. First we establish that the map defined in [L, §40.2.5 (a)] is an isomorphism for certain admissible sequences. Second we show the map gives rise to a convex basis of Poincaré–Birkhoff–Witt (PBW) type for U, an affine untwisted quantized enveloping algebra of Drinfeld and Jimbo. The computations in this paper are made possible by extending the usual braid group actio...
متن کاملAffine maps between quadratic assignment polytopes and subgraph isomorphism polytopes
We consider two polytopes. The quadratic assignment polytope QAP(n) is the convex hull of the set of tensors x⊗x, x ∈ Pn, where Pn is the set of n×n permutation matrices. The second polytope is defined as follows. For every permutation of vertices of the complete graph Kn we consider appropriate (n 2 ) × (n 2 ) permutation matrix of the edges of Kn. The Young polytope P ((n − 2, 2)) is the conv...
متن کاملRandom Polytopes and Affine Surface Area
Let K be a convex body in R. A random polytope is the convex hull [x1, ..., xn] of finitely many points chosen at random in K. E(K,n) is the expectation of the volume of a random polytope of n randomly chosen points. I. Bárány showed that we have for convex bodies with C3 boundary and everywhere positive curvature c(d) lim n→∞ vold(K)− E(K,n) ( vold(K) n ) 2 d+1 = ∫ ∂K κ(x) 1 d+1 dμ(x) where κ(...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Selecta Mathematica
سال: 2018
ISSN: 1022-1824,1420-9020
DOI: 10.1007/s00029-018-0436-9