On the geometric realization of the inner product and canonical basis for quantum affine $\mathfrak{sl}_n$

Details On the geometric realization of the inner product and canonical basis for quantum affine $\mathfrak{sl}_n$ On the geometric realization of the inner product and canonical basis for quantum affine $\mathfrak{sl}_n$

2010-09-27

arxiv.org/abs/1009.5411v1

Mathematics

Quantum Algebra

Scientific paper

We give a geometric interpretation of the inner product on the modified
quantum group of $\hat{\mathfrak{sl}}_n$. We also give some applications of
this interpretation, including a positivity result for the inner product, and a
new geometric construction of the canonical basis.

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