Two-Parameter Quantum Algebras, Canonical Bases, and Categorifications
نویسندگان
چکیده
منابع مشابه
Canonical Bases for Quantum Generalized Kac-moody Algebras
We construct canonical bases for quantum generalized Kac-Moody algebras using semisimple perverse sheaves.
متن کاملAddendum to “canonical Bases for Quantum Generalized Kac-moody Algebras”
We provide some necessary details to several arguments appearing in our previous paper “Canonical bases for quantum generalized Kac-Moody algebras”. As pointed out to us by several people, some of the arguments in our paper [KS] are too sketchy and at places incomplete. The first purpose of this addendum is to fill in the missing details and provide complete proofs. The second purpose is to exp...
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(1) Each element of B is a product of a monomial in ‘real root vectors’ and a Schur function in ‘imaginary root vectors’. (2) The transition matrix between B and Kashiwara–Lusztig’s global crystal basis (or canonical basis) G(B(−∞)) is upper-triangular with 1’s on the diagonal (with respect to a certain explicitly defined ordering) and with above diagonal entries in q s Z[q −1 s ]. When g is sy...
متن کاملCanonical bases for subalgebras of factor algebras
We introduce canonical bases for subalgebras of quotients of the commutative and non-commutative polynomial ring. The usual theory for Gröbner bases and its counterpart for subalgebras of polynomial rings, also called SAGBI bases, are combined to obtain a tool for computation in subalgebras of factor algebras.
متن کاملConstructing Canonical Bases of Quantized Enveloping Algebras
Since the invention of canonical bases of quantized enveloping algebras, one of the main problems has been to establish what they look like. Explicit formulas are only known in a few cases corresponding to root systems of low rank, namely A1 (trivial), A2 ([Lusztig 90]), A3 ([Xi 99a]), and B2 ([Xi 99b]). Furthermore, there is evidence suggesting that for higher ranks the formulas become so comp...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2014
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnu159