Seminar in Representation Theory
Lusztig's periodic R-polynomials and a dual basis in the quantum K-theory of the flag manifold
2026/10/15 (Thu.) 14:00~15:00
- Date : 2026/10/15 (Thu.) 14:00~15:00
- Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
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Speaker : Satoshi Naito (Tokyo Institute of Technology)
- Organizer : Ching Hung Lam (AS)
- Abstract :
In the (torus-equivariant) quantum K-theory ring $QK_{H}(X)$
of the full flag manifold $X = G/B$, we consider the basis $I^{w}_{Q}, w
\in W$, dual to the Schubert classes $O_{w}, w \in W$, with respect to
the quantum K-metric. In this talk, as an application of a
combinatorial formula for Lusztig's periodic R-polynomials, we give an
explicit formula for the expansion of the quantum dual basis $I^{w}_{Q}$
above by the opposite Schubert classes $O^{v}, v \in W$, in terms of the
quantum Bruhat graph.
Our main ingredient in the proof of this expansion formula is the
Moebius inversion for the semi-infinite (or generic) Bruhat order on
the affine Weyl group associated to the simple, simply-connected,
complex algebraic group G. This talk is based on joint works with H.
Watanabe and L. C. Mihalcea.
