On the generalised Dipper–James–Murphy conjecture in quantum characteristic 2

Jun Hu; Kai Zhou; Danni Wang

doi:10.1007/s00605-016-0920-2

On the generalised Dipper–James–Murphy conjecture in quantum characteristic 2

Jun Hu^*
, Kai Zhou
, Danni Wang

^*Corresponding author for this work

Zhejiang University
Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Let r , n be natural numbers. Let e≠ 1 be a non-negative integer and v₁, ⋯ , v_r∈ Z. Let K_r(n) be the set of Kleshchev multipartitions of n with respect to (e; Q) , where Q: = (v₁+ eZ, ⋯ , v_r+ eZ) ∈ (Z/ eZ) ^r. The generalised Dipper–James–Murphy conjecture asserts that the set K_r(n) coincides with the set of (Q, e) -restricted multipartitions of n. In this paper we prove this conjecture in the case when e= 2. Furthermore, we show that in this case the set K_r(n) also coincides with the set of ladder multipartitions of n as well as with the set of strong ladder multipartitions of n.

Original language	English
Pages (from-to)	629-642
Number of pages	14
Journal	Monatshefte fur Mathematik
Volume	181
Issue number	3
DOIs	https://doi.org/10.1007/s00605-016-0920-2
Publication status	Published - 1 Nov 2016
Externally published	Yes

Keywords

Kleshchev multipartitions
Ladder multipartitions
Ladder nodes

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10.1007/s00605-016-0920-2

Cite this

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title = "On the generalised Dipper–James–Murphy conjecture in quantum characteristic 2",

abstract = "Let r , n be natural numbers. Let e≠ 1 be a non-negative integer and v1, ⋯ , vr∈ Z. Let Kr(n) be the set of Kleshchev multipartitions of n with respect to (e; Q) , where Q: = (v1+ eZ, ⋯ , vr+ eZ) ∈ (Z/ eZ) r. The generalised Dipper–James–Murphy conjecture asserts that the set Kr(n) coincides with the set of (Q, e) -restricted multipartitions of n. In this paper we prove this conjecture in the case when e= 2. Furthermore, we show that in this case the set Kr(n) also coincides with the set of ladder multipartitions of n as well as with the set of strong ladder multipartitions of n.",

keywords = "Kleshchev multipartitions, Ladder multipartitions, Ladder nodes",

author = "Jun Hu and Kai Zhou and Danni Wang",

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year = "2016",

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doi = "10.1007/s00605-016-0920-2",

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TY - JOUR

T1 - On the generalised Dipper–James–Murphy conjecture in quantum characteristic 2

AU - Hu, Jun

AU - Zhou, Kai

AU - Wang, Danni

PY - 2016/11/1

Y1 - 2016/11/1

N2 - Let r , n be natural numbers. Let e≠ 1 be a non-negative integer and v1, ⋯ , vr∈ Z. Let Kr(n) be the set of Kleshchev multipartitions of n with respect to (e; Q) , where Q: = (v1+ eZ, ⋯ , vr+ eZ) ∈ (Z/ eZ) r. The generalised Dipper–James–Murphy conjecture asserts that the set Kr(n) coincides with the set of (Q, e) -restricted multipartitions of n. In this paper we prove this conjecture in the case when e= 2. Furthermore, we show that in this case the set Kr(n) also coincides with the set of ladder multipartitions of n as well as with the set of strong ladder multipartitions of n.

AB - Let r , n be natural numbers. Let e≠ 1 be a non-negative integer and v1, ⋯ , vr∈ Z. Let Kr(n) be the set of Kleshchev multipartitions of n with respect to (e; Q) , where Q: = (v1+ eZ, ⋯ , vr+ eZ) ∈ (Z/ eZ) r. The generalised Dipper–James–Murphy conjecture asserts that the set Kr(n) coincides with the set of (Q, e) -restricted multipartitions of n. In this paper we prove this conjecture in the case when e= 2. Furthermore, we show that in this case the set Kr(n) also coincides with the set of ladder multipartitions of n as well as with the set of strong ladder multipartitions of n.

KW - Kleshchev multipartitions

KW - Ladder multipartitions

KW - Ladder nodes

UR - https://www.scopus.com/pages/publications/84969246788

U2 - 10.1007/s00605-016-0920-2

DO - 10.1007/s00605-016-0920-2

M3 - Article

AN - SCOPUS:84969246788

SN - 0026-9255

VL - 181

SP - 629

EP - 642

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

IS - 3

ER -

On the generalised Dipper–James–Murphy conjecture in quantum characteristic 2

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Keywords

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