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| XXXIX Workshop on Geometric Methods in Physics | 19.06–25.06.2022 |
| XI School on Geometry and Physics | 27.06–1.07.2022 |
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Tomasz CzyżyckiGeneralized Transforms of Affine Weyl GroupsDiscrete transforms of Weyl orbit functions on finite fragments of shifted dual root lattices are established. The congruence classes of the dual weight lattices intersected with the fundamental domains of the affine Weyl groups constitute the point sets of the transforms. The shifted weight lattices intersected with the fundamental domains of the extended dual affine Weyl groups form the sets of labels of Weyl orbit functions. The coinciding cardinality of the point and label sets and the corresponding discrete orthogonality relations of Weyl orbit functions are demonstrated. The forward and backward discrete Fourier–Weyl transforms together with the associated interpolation and Plancherel formulas are presented. The unitary transform matrices of the discrete transforms are exemplified for the case $A_2$. |
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| University of Bialystok |
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