Noncommutative Pfaffians associated with the orthogonal algebra

Артамонов, Д. В.; Golubeva, V. A.

doi:10.1070/sm2012v203n12abeh004283

Cited by 4 publications

(8 citation statements)

References 20 publications

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“…The elements C k are called the Capelli elements. In the paper [2] the commutation relations between pfaffians P f F I and generators were found. To formulate them let us define F ij I.…”

Section: Noncommutative Pfaffians and Capelli Elementsmentioning

confidence: 99%

“…Доказательство. The following formula takes place which is a particular case of the minor summation formula [2] P f F I = 1 2…”

Section: Representation Of C −1 4 As a Differential Operatormentioning

confidence: 99%

“…Thus it is not an OPE of type (2): when one takes the OPE the field J α (z) removes J α from the normal order product (J α (J β J γ ))(w) and one obtains (J β J γ )(w).…”

Section: Introductionmentioning

confidence: 99%

“…From this notation the following conjecture arises. To obtain the OPE of type (2), it is necessary to take a field ϕ α (z) and a higher analog of the energy momentum tensor of type W (w) = α (ϕ α ϕ α )(w). In particular the corresponding central element is a sum of squares α ϕ α ϕ α .…”

Section: Introductionmentioning

confidence: 99%

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W-algebras and higher analogues of the Knizhnik-Zamolodchikov equations

Артамонов

Golubeva

2015

Theor Math Phys

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АннотацияThe key role in the derivation of the Knizhnik-Zamolodchikov equations in the W ZW -theory is played by the energy-momentum tensor, that is constructed from a central Casimir element of the second order in a universal enveloping algebra of a corresponding Lie algebra. In the paper a possibility of construction of analogs of Knizhnik-Zamolodchikov equations using higher order central elements is investigated. The Gelfand elements of the third order for a simple Lie algebra of series A and Capelli elements of the fourth order for the a simple Lie algebra of series B, D are considered. In the first case the construction is not possible a the second case the desired equation is derived.(68) From here one gets (P f F J ) m P f F I = 0, m > 2.(69)

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“…The elements C k are called the Capelli elements. In the paper [2] the commutation relations between pfaffians P f F I and generators were found. To formulate them let us define F ij I.…”

Section: Noncommutative Pfaffians and Capelli Elementsmentioning

confidence: 99%

“…Доказательство. The following formula takes place which is a particular case of the minor summation formula [2] P f F I = 1 2…”

Section: Representation Of C −1 4 As a Differential Operatormentioning

confidence: 99%

“…Thus it is not an OPE of type (2): when one takes the OPE the field J α (z) removes J α from the normal order product (J α (J β J γ ))(w) and one obtains (J β J γ )(w).…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

W-algebras and higher analogues of the Knizhnik-Zamolodchikov equations

Артамонов

Golubeva

2015

Theor Math Phys

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“…In [6] we have constructed Knizhnik-Zamolodchikov type equations for the root system A, but our construction was based on special centra elements in the universal enveloping algebra of the orthogoanl algebra, namely the Capelli elements. In the present paper we generalize our construction to the root system B and show that the construction from [6] can be in fact interpreted in some sence as a very special case of the general Leibman's construction. This is a system of type…”

Section: Introductionmentioning

confidence: 99%

Knizhnik-Zamolodchikov type equations for the root systemBand Capelli central elements

Артамонов¹,

Golubeva²

2014

J. Phys.: Conf. Ser.

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The construction of the well-known Knizhnik-Zamolodchikov equations uses the central element of the second order in the universal enveloping algebra for some Lie algebra. But in the universal enveloping algebra there are central elements of higher orders. It seems desirable to use these elements for the construction of Knizhnik-Zamolodchikov type equations. In the present paper we give a construction of such Knizhnik-Zamolodchikov type equations for the root system B associated with Capelli central elements in the universal enveloping algebra for the orthogonal algebra.

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$W$-Алгебры И Высшие Аналоги Уравнения Книжника - Замолодчикова

Артамонов¹,

Golubeva²

2015

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Noncommutative Pfaffians associated with the orthogonal algebra

Cited by 4 publications

References 20 publications

W-algebras and higher analogues of the Knizhnik-Zamolodchikov equations

W-algebras and higher analogues of the Knizhnik-Zamolodchikov equations

Knizhnik-Zamolodchikov type equations for the root systemBand Capelli central elements

$W$-Алгебры И Высшие Аналоги Уравнения Книжника - Замолодчикова

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