Combinatorics of \(\mathcal H\)-primes in quantum matrices

DOI10.1016/j.jalgebra.2006.10.023zbMath1172.05051arXivmath/0501010OpenAlexW2142821099MaRDI QIDQ875079

Stephane Launois

Publication date: 11 April 2007

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0501010

zbMATH Keywords

quantum matricesprime idealsBruhat orderquantum minors

Mathematics Subject Classification ID

Related Items (21)

On \(q\)-poly-Bernoulli numbers arising from combinatorial interpretations ⋮ Bruhat intervals as rooks on skew Ferrers boards ⋮ Poly-Bernoulli numbers and polynomials with a \(q\) parameter ⋮ From Grassmann necklaces to restricted permutations and back again ⋮ Toppling on permutations with an extra chip ⋮ Totally nonnegative cells and matrix Poisson varieties ⋮ Total Positivity is a Quantum Phenomenon: The Grassmannian Case ⋮ Multidimensional matrices uniquely recovered by their lines ⋮ Matrices uniquely determined by their lonesums ⋮ The Dixmier-Moeglin equivalence for Leavitt path algebras. ⋮ Generalizations of poly-Bernoulli and poly-Cauchy numbers ⋮ The FRT-construction via quantum affine algebras and smash products. ⋮ Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves. ⋮ Enumeration of \(\mathcal H\)-strata in quantum matrices with respect to dimension ⋮ Quantum Schubert cells via representation theory and ring theory ⋮ Explicit formula for generalization of poly-Bernoulli numbers and polynomials with a,b,c parameters ⋮ A graph theoretic method for determining generating sets of prime ideals in quantum matrices ⋮ Combinatorial properties of poly-Bernoulli relatives ⋮ Admissible diagrams in quantum nilpotent algebras and combinatoric properties of Weyl groups ⋮ Dimension and enumeration of primitive ideals in quantum algebras. ⋮ A STUDY OF POLY-BERNOULLI POLYNOMIALS ASSOCIATED WITH HERMITE POLYNOMIALS WITH q-PARAMETER

Cites Work

• Poisson structures on affine spaces and flag varieties. I: Matrix affine Poisson space.
• Primitive ideals of \({\mathbf C}_ q[SL(3)\)]
• Primitive ideals of \(\mathbb{C}_ q[SL(n)\)]
• Poly-Bernoulli numbers
• The invariant prime ideals of \(O_q({\mathcal M}_{m,p}(\mathbb{C}))\).
• Lectures on algebraic quantum groups
• Vanishing of derivations and prime spectra of quantum algebras
• Prime spectrum of \(O_q(M_n(k))\): canonical image and normal separation
• Winding-invariant prime ideals in quantum \(3\times 3\) matrices.
• The quantum coordinate ring of the special linear group
• Prime Factor Algebras of the Coordinate Ring of Quantum Matrices
• GENERATORS FOR $\mathcal{H}$-INVARIANT PRIME IDEALS IN $O_{q}(\mathcal{M}_{m,p}(\mathbb{C}))$
• RANKtℋ-PRIMES IN QUANTUM MATRICES
• The Dixmier-Moeglin equivalence in quantum coordinate rings and quantized Weyl algebras
• PRIME IDEALS INVARIANT UNDER WINDING AUTOMORPHISMS IN QUANTUM MATRICES
• Prime spectra of quantum semisimple groups
• Quantum linear groups
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