Plethystic exponential calculus and characteristic polynomials of permutations

Florentino, Carlos A. A.

doi:10.48550/arxiv.2105.13049

Cited by 3 publications

(3 citation statements)

References 5 publications

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“…with ψ 0 (z) ≡ 1. By [Fl,Thm 3.1], the generating series for the ψ n (z) is now the plethystic exponential 1 + n≥1 ψ n (z)…”

Section: Thus We Concludementioning

confidence: 99%

Mixed Hodge structures on character varieties of nilpotent groups

Florentino¹,

Lawton²,

Silva³

2021

Preprint

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Let Hom 0 (Γ, G) be the connected component of the identity of the variety of representations of a finitely generated nilpotent group Γ into a connected reductive complex affine algebraic group G. We determine the mixed Hodge structure on the representation variety Hom 0 (Γ, G) and on the character variety Hom 0 (Γ, G)/ /G. We obtain explicit formulae (both closed and recursive) for the mixed Hodge polynomial of these representation and character varieties.

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“…with ψ 0 (z) ≡ 1. By [Fl,Thm 3.1], the generating series for the ψ n (z) is now the plethystic exponential 1 + n≥1 ψ n (z)…”

Section: Thus We Concludementioning

confidence: 99%

Mixed Hodge structures on character varieties of nilpotent groups

Florentino¹,

Lawton²,

Silva³

2021

Preprint

View full text Add to dashboard Cite

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“…The reader is also referred to[26,27] for a plethystic programme for counting BPS operators in quiver gauge theories, though we emphasize that what we study here is in a different context. For further disscussions on PE, see[28,29].…”

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confidence: 99%

Crystal melting, BPS quivers and plethystics

Bao

2022

J. High Energ. Phys.

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We study the refined and unrefined crystal/BPS partition functions of D6-D2-D0 brane bound states for all toric Calabi-Yau threefolds without compact 4-cycles and some non-toric examples. They can be written as products of (generalized) MacMahon functions. We check our expressions and use them as vacuum characters to study the gluings. We then consider the wall crossings and discuss possible crystal descriptions for different chambers. We also express the partition functions in terms of plethystic exponentials. For ℂ3 and tripled affine quivers, we find their connections to nilpotent Kac polynomials. Similarly, the partition functions of D4-D2-D0 brane bound states can be obtained by replacing the (generalized) MacMahon functions with the inverse of (generalized) Euler functions.

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mentioning

confidence: 99%

Crystal Melting, BPS Quivers and Plethystics

Bao,

He,

Zahabi

2022

Preprint

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We study the refined and unrefined crystal/BPS partition functions of D6-D2-D0 brane bound states for all toric Calabi-Yau threefolds without compact 4-cycles and some non-toric examples. They can be written as products of (generalized) MacMahon functions. We check our expressions and use them as vacuum characters to study the gluings. We then consider the wall crossings and discuss possible crystal descriptions for different chambers. We also express the partition functions in terms of plethystic exponentials. For C 3 and tripled affine quivers, we find their connections to nilpotent Kac polynomials. Similarly, the partition functions of D4-D2-D0 brane bound states can be obtained by replacing the (generalized) MacMahon functions with the inverse of (generalized) Euler functions.

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Plethystic exponential calculus and characteristic polynomials of permutations

Cited by 3 publications

References 5 publications

Mixed Hodge structures on character varieties of nilpotent groups

Mixed Hodge structures on character varieties of nilpotent groups

Crystal melting, BPS quivers and plethystics

Crystal Melting, BPS Quivers and Plethystics

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