Dual canonical bases and Kazhdan–Lusztig polynomials
نویسندگان
چکیده
منابع مشابه
On Dual Canonical Bases
The dual basis of the canonical basis of the modified quantized enveloping algebra is studied, in particular for type A. The construction of a basis for the coordinate algebra of the n × n quantum matrices is appropriate for the study the multiplicative property. It is shown that this basis is invariant under multiplication by certain quantum minors including the quantum determinant. Then a bas...
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In this paper, the singularity Ringel-Hall algebras are defined. A new class of perverse sheaves are shown to have purity property. The canonical bases of singularity RingelHall algebras are constructed. As an application, the existence of Hall polynomials in the tame quiver algebras is proved.
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The polynomial ring Z[x11, . . . , x33] has a basis called the dual canonical basis whose quantization facilitates the study of representations of the quantum group Uq(sl3(C)) [8] [5]. On the other hand, Z[x11, . . . , x33] inherits a basis from the cluster monomial basis of a geometric model of the type D4 cluster algebra [3] [4]. We prove that these two bases are equal. This extends work of S...
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Rosso and Green have shown how to embed the positive part Uq(n) of a quantum enveloping algebra Uq(g) in a quantum shuffle algebra. In this paper we study some properties of the image of the dual canonical basis B∗ of Uq(n) under this embedding Φ. This is motivated by the fact that when g is of type Ar, the elements of Φ(B∗) are q-analogues of irreducible characters of the affine Iwahori-Hecke ...
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We compare two natural bases for the invariant space of a tensor product of irreducible representations of A2, or sl(3). One basis is the web basis, defined from a skein theory called the combinatorial A2 spider. The other basis is the dual canonical basis, the dual of the basis defined by Lusztig and Kashiwara. For sl(2) or A1, the web bases have been discovered many times and were recently sh...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2006
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2006.01.053