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- W2119744710 abstract "Hecke proved that the theta series of a positive definite even unimodular lattice is a polynomial of the well-known Essenstein series E 4 (z) and the Ramanujan series Δ 24 (z). A natural question is what kind of polynomials in E 4 (z) and Δ 24 (z) could be the theta series of positive definite even unimodular lattices. In this paper, we find two combinatorial identities on the theta series of the root lattices of the finite-dimensional simple Lie algebras of type D 4n and the cosets in their integral duals, in terms of E 4 (z) and Δ 24 (z). Using these two identities, we prove that three families of weighted symmetric polynomials of two fixed families of polynomials of E 4 (z) and Δ 24 (z) are the theta series of certain positive definite even unimodular lattices, obtained by gluing finitely many copies of the root lattices of the finite-dimensional simple Lie algebras of type D 2n . The results also show that the full permutation groups are the hidden symmetry of the theta series of certain unimodular lattices." @default.
- W2119744710 created "2016-06-24" @default.
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- W2119744710 date "2006-03-01" @default.
- W2119744710 modified "2023-10-14" @default.
- W2119744710 title "Theta Series of Unimodular Lattices, Combinatorial Identities and Weighted Symmetric Polynomials" @default.
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- W2119744710 doi "https://doi.org/10.1142/s1005386706000101" @default.
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