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Theoretical analysis reveals an atomic decomposition for the spherical Hecke algebra in type G2, suggesting an algorithmic method to compute generalized Kostka–Foulkes polynomials.
We show that the elements of the Kazhdan–Lusztig basis of the spherical Hecke algebra of type have an atomic decomposition. As a by‐product, we obtain a new algorithm to compute generalized Kostka–Foulkes polynomials in type .
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Muniz et al. (2026) studied this question.
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