Pure and Applied Mathematics Quarterly

Volume 16 (2020)

Number 3

Special Issue: In Honor of Prof. Kyoji Saito’s 75th Birthday

Guest Editors: Stanislaw Janeczko, Si Li, Jie Xiao, Stephen S.T. Yau, and Huaiqing Zuo

Invariants of the Weyl group of type $A^{(2)}_{2l}$

Pages: 337 – 369

DOI: https://dx.doi.org/10.4310/PAMQ.2020.v16.n3.a2


Kenji Iohara (Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, Villeurbanne, France)

Yoshihisa Saito (Department of Mathematics, Rikkyo University, Toshima-ku, Tokyo, Japan)


In this note, we show the polynomiality of the ring of invariants with respect to the Weyl group of type $A^{(2)}_{2l}$.


affile Lie algebra, affine root system of type $A^{(2)}_{2l}$, affine Weyl group, theta function associated with an odd lattice

2010 Mathematics Subject Classification

Primary 17B10, 17B67. Secondary 11F50.

At an early stage of this project, K.I. was partially supported by the program FY2018 JSPS Invitation. He is also partially supported by the French ANR (ANR project ANR-15-CE40-0012). Y.S. is partially supported by JSPS KAKENHI Grant Number 16K05055.

Received 1 March 2019

Accepted 27 June 2019

Published 11 November 2020