Super duality for quantum affine algebras of type $A$

Jae-Hoon Kwon; Sin-Myung Lee

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Super duality for quantum affine algebras of type $A$

Jae-Hoon Kwon, Sin-Myung Lee

Representation Theory · Submitted 13 Oct 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We explain how the representations of the quantum group of $\mathrm{L}\mathfrak{gl}_{M|N}$ are directly related to those of the quantum affine algebra of type $A$, using an exact monoidal functor called truncation.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,083 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.45 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We introduce a new approach to the study of finite-dimensional representations of the quantum group of the affine Lie superalgebra $\mathrm{L}\mathfrak{gl}_{M|N}=\mathbb{C}[t,t^{-1}]\otimes\mathfrak{gl}_{M|N}$ ($M\neq N$). We explain how the representations of the quantum group of $\mathrm{L}\mathfrak{gl}_{M|N}$ are directly related to those of the quantum affine algebra of type $A$, using an exact monoidal functor called truncation. This can be viewed as an affine analogue of super duality of type $A$.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We introduce a new approach to the study of finite-dimensional representations of the quantum group of the affine Lie superalgebra $\mathrm{L}\mathfrak{gl}_{M\|N}=\mathbb{C}[t,t^{-1}]\otimes\mathfrak{gl}_{M\|N}$ ($M\neq N$).	contribution 1.00	0.92	0.11	asserted 1.00
s1	We explain how the representations of the quantum group of $\mathrm{L}\mathfrak{gl}_{M\|N}$ are directly related to those of the quantum affine algebra of type $A$, using an exact monoidal functor called truncation.	contribution 0.57	0.86	0.45	asserted 1.00
s2	This can be viewed as an affine analogue of super duality of type $A$.	interpretation 1.00	0.49	0.22	hedged possibility 0.68

What kind of paper the classifier reports this is: method or tool 0.92 · evidence from proof or derivation 0.97.

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Original abstract

We introduce a new approach to the study of finite-dimensional representations of the quantum group of the affine Lie superalgebra $\mathrm{L}\mathfrak{gl}_{M|N}=\mathbb{C}[t,t^{-1}]\otimes\mathfrak{gl}_{M|N}$ ($M\neq N$). We explain how the representations of the quantum group of $\mathrm{L}\mathfrak{gl}_{M|N}$ are directly related to those of the quantum affine algebra of type $A$, using an exact monoidal functor called truncation. This can be viewed as an affine analogue of super duality of type $A$.

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3 arXiv papers cite this in 11 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Compares with it 1 paper

(1) The isomorphism in [ref] is given between the quantum affine superalgebra and $()$ extended by $Σ$, while the subalgebras generated by $k_μ, K_μ$ $(μ∈P)$ are slightly different from the ones here.

Affinization of $q$-oscillator representations of $U_q(\mathfrak{gl}_n)$ · Lie superalgebras and classical limits · 0.94

Cites it as background 1 paper

Let us first recall the notion of the generalized quantum groups (of affine type $A$) [ref] , which is also closely related to the quantum affine superalgebras (cf. [ref] ).

Affinization of $q$-oscillator representations of $U_q(\mathfrak{gl}_n)$ · Generalized quantum group $U()$ · 1.00

What it cites · 8 sentences without a confident label

Builds on 1 paper

The isomorphism is a generalization of the one in [ref] (see also [ref] ), where the map is defined only on the subalgebra of finite type generated by $K_μ$ ($μ∈P$), $E_i,F_i$ ($i∈I∖{0}$) and $σ_j$ ($j∈𝕀$), and $$ is assumed to be standard, that is, $=_M|N$.

Kirillov-Reshetikhin modules of generalized quantum group of type $A$ · Quantum affine superalgebra · 0.84

Uses the method or tool of 1 paper

We follow the presentation [ref] .

Notes on Restricted Inverse Limits of Categories · Inverse limit category · 0.85

Cites as support 1 paper

Then by [ref] , any non-zero $tr_k(𝕍)$ is irreducible.

Notes on Restricted Inverse Limits of Categories · Equivalence between $R^J-mod_0$ and $C_J(^∞)$ · 0.97

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