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Keywords
(9)
Algebraic Geometry
Flag Manifold
Indexation
Lie Algebra
Quantum Algebra
Representation Theory
Spectrum
Stratification
Weyl Group
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Primitive ideals in quantum Schubert cells: dimension of the strata
Primitive ideals in quantum Schubert cells: dimension of the strata,Jason Bell,Karel Casteels,Stéphane Launois
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Primitive ideals in quantum Schubert cells: dimension of the strata
(
Citations: 1
)
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Jason Bell
,
Karel Casteels
,
Stéphane Launois
The aim of this paper is to study the
representation theory
of quantum Schubert cells. Let $\g$ be a simple complex Lie algebra. To each element $w$ of the
Weyl group
$W$ of $\g$, De Concini, Kac and Procesi have attached a subalgebra $U_q[w]$ of the quantised enveloping algebra $U_q(\g)$. Recently, Yakimov showed that these algebras can be interpreted as the quantum Schubert cells on quantum flag manifolds. In this paper, we study the primitive ideals of $U_q[w]$. More precisely, it follows from the
Stratification
Theorem of Goodearl and Letzter that the primitive
spectrum
of $U_q[w]$ admits a
stratification
indexed by those primes that are invariant under a natural torus action. Moreover each stratum is homeomorphic to the
spectrum
of maximal ideals of a torus. The main result of this paper gives an explicit formula for the dimension of the stratum associated to a given torusinvariant prime.
Published in 2010.
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References
(18)
Enumeration of $\C{H}$strata in quantum matrices with respect to dimension
(
Citations: 2
)
Jason Bell
,
Karel Casteels
,
Stéphane Launois
Published in 2010.
On the dimension of Hstrata in quantum matrices
(
Citations: 1
)
J. Bell
,
S. Launois
Published in 2009.
An automatontheoretic approach to the representation theory of quantum algebras
(
Citations: 5
)
J. Bell
,
S. Launois
,
J. Lutley
Journal:
Advances in Mathematics  ADVAN MATH
, vol. 223, no. 2, pp. 476510, 2010
Dimension and enumeration of primitive ideals in quantum algebras
(
Citations: 6
)
J. Bell
,
S. Launois
,
N. Nguyen
Journal:
Journal of Algebraic Combinatorics  J ALGEBR COMB
, vol. 29, no. 3, pp. 269294, 2009
PRIME SPECTRA OF QUANTUM SEMISIMPLE GROUPS
(
Citations: 31
)
K. A. BROWN
,
K. R. GOODEARL
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Citations
(1)
The DixmierMoeglin Equivalence for Leavitt Path Algebras
Gene Abrams
,
Jason P. Bell
,
Kulumani M. Rangaswamy
Journal:
Algebras and Representation Theory  ALGEBR REPRESENT THEORY
, pp. 119