Differential forms via the Bernstein–Gelfand–Gelfand resolution for quantized irreducible flag manifolds
نویسندگان
چکیده
منابع مشابه
Differential forms via the Bernstein-Gelfand-Gelfand resolution for quantized irreducible flag manifolds
The quantum group version of the Bernstein-Gelfand-Gelfand resolution is used to construct a double complex of Uq(g)-modules with exact rows and columns. The locally finite dual of its total complex is identified with the de Rham complex for quantized irreducible flag manifolds. MSC: 17B37, 58B32
متن کاملDe Rham Complex for Quantized Irreducible Flag Manifolds
It is shown that quantized irreducible flag manifolds possess a canonical q-analogue of the de Rham complex. Generalizing the well known situation for the standard Podleś’ quantum sphere this analogue is obtained as the universal differential calculus of a distinguished first order differential calculus. The corresponding differential d can be written as a sum of differentials ∂ and ∂. The univ...
متن کاملThe Locally Finite Part of the Dual Coalgebra of Quantized Irreducible Flag Manifolds
The notion of locally finite part of the dual coalgebra of certain quantized coordinate rings is introduced. In the case of irreducible flag manifolds this locally finite part is shown to coincide with a natural quotient coalgebra U of Uq(g). On the way the coradical filtration of U is determined. A graded version of the duality between U and the quantized coordinate ring is established. This l...
متن کاملPoisson Structures on Complex Flag Manifolds Associated with Real Forms
For a complex semisimple Lie group G and a real form G0 we define a Poisson structure on the variety of Borel subgroups of G with the property that all G0-orbits in X as well as all Bruhat cells (for a suitable choice of a Borel subgroup of G) are Poisson submanifolds. In particular, we show that every non-empty intersection of a G0-orbit and a Bruhat cell is a regular Poisson manifold, and we ...
متن کاملThe Pieri Formula for Flag Manifolds
We show the equivalence of the Pieri formula for ag manifolds with certain identities among the structure constants for the Schubert basis of the polynomial ring. This gives new proofs of both the Pieri formula and of these identities. A key step is the association of a symmetric function to a nite poset with labeled Hasse diagram satisfying a symmetry condition. This gives a uniied deenition o...
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: Journal of Geometry and Physics
سال: 2007
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2007.07.005